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SYSC 4405 - Digital Signal Processing

Midterm #2: Material is 2−12,14−25
Midterm #1 (with solutions): V1 V2 Midterm #2 (with solutions): [pdf] Marks (by last 3 digits of student number)

Description

Discrete time signal and system representation: time domain, z-transform, frequency domain. Sampling theorem. Digital filters: design, response, implementation, computer-aided design. Spectral analysis: the discrete Fourier transform and the FFT. Applications of digital signal processing.

Prerequisites

SYSC 2500 or SYSC 3500 or SYSC 3600.
Students who have not satisfied the perquisites for this course must either a) withdraw from the course, or b) fill out a prerequisite waiver from www.sce.carleton.ca/ughelp, or c) may be deregistered from the course after the last day to register for courses in the term.

Instructor

Andy Adler
Email: adler@sce.carleton.ca Note: Emails to the instructor must contain a subject line "SYSC4405: your subject line"
Office: Canal 6204
Phone: +1-613-520-2600 x 8785
Office Hours:  Thursday 1315−1445

Teaching Assistants

T.A.: Patrick Quesnel,       Kun Wang
Email: patrickquesnel@cmail.carleton.ca KunWang@cmail.carleton.ca
Office   Canal 6107 ME 4324
Office Hours:   Thurs 11:30−12:30 Tues 10:00−11:00

Times and Locations

Fall 2012     (Sept. 10 − Dec. 3)

Section  Activity  Day  Time  Location 
SYSC4405    LEC    Mon    13:05−14:25    TB 238   
   LEC    Wed    13:05−14:25    TB 238   
   LAB 1    Mon (even weeks, starting Sept.17)    14:35−17:25    Canal 5107   
   LAB 1    Tues (Odd weeks, starting Sept.11)    14:35−17:25    Canal 5107   
   LAB 1    Thur (Odd weeks, starting Sept.13)    14:35−17:25    Canal 5107   

Text

The text for this course will be the course slides. Links to course slides are given on the corresponding schedule.

Recommended suplementary material.

  • Monson H. Hayes, Digital Signal Processing, Schaum's Outlines, McGrawa-Hill
  • Steven W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing California Technical Publishing
  • Additional Reference: Course Notes (2006), Richard Dansereau
  • Marks

    Work  Value
    Quizzes (in Lab)    15%
    Laboratories    15%
    Midterm Exams (#1 & #2)    15%
    Final Exam    40%

    Marks Policies

    • Weighting of midterm and final will be optimized within the range given to maximize student benefit.
    • Late work Policy (without *excellent* excuse): 1) 20% if ≤ 7 days late, 2) 0 mark if > 7 days late.
    • If you have a question about a mark you have received, fill out, sign and submit this form.

    Students with Disabilities

      The Paul Menton Centre for Students with Disabilities (PMC) provides services to students with Learning Disabilities (LD), psychiatric/mental health disabilities, Attention Deficit Hyperactivity Disorder (ADHD), Autism Spectrum Disorders (ASD), chronic medical conditions, and impairments in mobility, hearing, and vision. If you have a disability requiring academic accommodations in this course, please contact PMC at 613-520-6608 or pmc@carleton.ca for a formal evaluation. If you are already registered with the PMC, contact your PMC coordinator to send me your Letter of Accommodation at the beginning of the term, and no later than two weeks before the first in-class scheduled test or exam requiring accommodation. After requesting accommodation from PMC, meet with me to ensure accommodation arrangements are made. Please consult the PMC website for the deadline to request accommodations for the formally-scheduled exam.

    Exams (Midterm and Final)

    Quizzes

    Quizzes take place in the first 15 minutes of each lab session. Each quiz will be one question from the corresponding list below:
     
    No.  Assignment  Due Date
    1   No quiz for this lab   Sep. 11 (LAB1O)
    Sep. 13 (LAB2O)
    Sep. 17 (LAB1E)
     

    2  
    1. Characterize whether following systems are: a) Linear, b) Shift Invariant, c) Memoryless, d) LSI, e) Causal, f) Stable:
      1. y[n]= 8x[n] + 2
      2. y[n]= x[n] + x[n−2] + x[n−4] + x[n−6] + x[n−8] + …
      3. y[n]= x[n] + x[0]
      4. y[n]= 0
      5. y[n]= 2x[n²]
      6. y[n]= (x[n²])²
    2. Given the sequence, x[n]
      x[n] = 2δ[n+3] + (3−n)(u[n]−u[n−3])
      sketch the following sequences (for −2≤n≤8):
      1. y1[n] = x[2n−3]
      2. y2[n] = x[|n|]
    3. An LSI system responds to a step input (u[n]) with output (g[n]). Calculate the unit sample (impulse) response as a function of g[n].
    4. Can a LSI system be characterized completely by its reponse to one test input signal? However, in practice, it is not a good idea to only use one test to characterize a system. Briefly (<50 words) describe why not
    5. A system is described by the LCCDE
      y[n] − y[n−1] + y[n−2] = x[n−3]
      The input is x[n] = n(u[n]−u[n−4]); initial conditions are y[−3] = 2 and y[−4] = 1. Show the response of the system from n=−2 to n=+8.
    6. Q2 from Final 2011,
    7. Q3 from Final 2011,
    8. Q5 from Final 2011,
      Sep. 25 (LAB1O)
    Sep. 27 (LAB2O)
    Oct. 1 (LAB1E)
     

    3   Background: You're building a portable music recorder and playback system. The system has recorded a sample sound for playback. The input, x(t), at the microphone is:
    x(t)= 10 sin(600πt) + 5 sin(4100πt) mV
    1. Show the Fourier transform, X(Ω), as a phasor plot.
    2. Without using any type of anti-aliasing filter, the signal is sampled at 1000 samples/s, giving a sampled sequence x[n]. Calculate x[n] showing each term in its lowest frequency form.
    3. Calculate the Nyquist frequency for this sampling rate, and calculate at what frequency the aliased representation of sin(4100πt) will appear in the sampled signal. Is this signal aliased?
    4. Calculate the value of x[n] for n = 0 … 3 .
    5. Input x[n] is sent into two filters:
        Filter 1: y = f1(x):           y1[n] = ½( x[n] + x[n−1] )
        Filter 2: y = f2(y):           y2[n] = ½( x[n] + y[n−1] )
      Show the block diagram for each filter. Calculate y1[n] and y2[n] for n = 0 … 3, and x[n] = δ[n]. Assume initial conditions are zero.
    6. Calculate the impulse response h1[n] and h2[n], for each filter
    7. Given two filters:
          f1: y[n] = 2x[n−1] + 3x[n−3]
          f2: y[n] = x[n−1] + 0.4y[n−1] f2
      The filters are combined in various ways. Calculate the impulse response of each filter, h1[n] and h2[n].
    8. Calculate the impulse response of the following combined filters, in terms of x[n]
                ______   ______
      i)  x --->| f1 |-->| f2 | ---> y
                ______   ______ 
      ii) x --->| f2 |-->| f1 | ---> y
                ______   __ 
      iii)x -+->| f2 |-->|+| ---> y
             |->| f1 |----^
      
      Oct. 9 (LAB1O)
    Oct. 11 (LAB2O)
    Oct. 15 (LAB1E)
     

    4   Consider the signal, x(t),
    x(t)= 5 cos(2π200t) + 4 cos(2π300t) + 3 cos(2π400t) + 2 cos(2π500t) mV
    1. Show the Fourier Transform phasor plot of x(t)
    2. Initially we sample x(t) at 700Hz. Calculate x[n]. Is the signal aliased?
    3. Show the Fourier Transform phasor plot of x[n]. Label each aliased component as "Folded" or "Non-folding".
    4. If we consider the aliased components to be noise, What is the signal to noise ratio? (recall that the power of each phasor component is ½×Amplitude²)
    5. Calculate the DTFT, X(ω), of: x[n]= u[n](0.1)n
    6. Calculate the DTFT, X(ω), of: x[n]= u[n](0.1)n cos( 0.1n )
    7. Q5 from Practice Midterm (F08),
    8. Q6 from Practice Midterm (F08),
    9. Q8 from Practice Midterm (F08),
      Oct. 23 (LAB1O)
    Oct. 25 (LAB2O)
    Oct. 29 (LAB1E)
     

    5a   Note: These quiz questions are designed to provide an example to practice for midterm #2. This is too long for an 80 minute midterm, but the questions will be similar. Questions marks "(not for quiz)" are for midterm practice, but not for the quiz 5A.
    1. A signal x(t) is zero everywhere except for the range 1.0s<t<1.001s, where it increases linearly from 0V to 1V. A DSP system samples the signal at FS=2.5kSamples/sec. Sketch the signal, x(t) and x[n] in range 1.0s<t<1.001s and indicate the values of n and x[n]
    2. Consider system S
      y[n] = 0.2x[n−2] + 0.3x[n−3] + 0.9y[n−1]
      Sketch a block diagram of this system (in the canonical form we saw in class)
    3. Consider the input x[n] = {1,2,3,4,0,0,0,0} and initial conditions y[−1] = 1. Calculate y[n] for 0≤n≤4 (to two signifcant figures).
    4. Calculate h[n] for System S
    5. Calculate H(ω) for System S
    6. We wish to calculate the convolution ( y[n]= h[n] * x[n] ) where
        x[n]= {2,4,6,8,10,12,14,18}
        h[n]= {2,−1}
      1. Using linear convolution, calculate y[0] and y[5]
      2. Sketch the convolution operation of the overlap-add method using N=4, M=2, and B=3.
      3. Calculate y[0] using circular convolution, using the overlap-add approach.
      4. Calculate y[5] using overlap-add with and using circular convolution.
      5. (not for quiz) Implement circular convolution using the DFT and IDFT of length N=4. Use this value to Calculate y[5]
    7. Given a DSP system with Ts=1ms, we need a band pass FIR filter, hBP[n], which will 1) Accept frequencies in the range 80−120Hz (to within 10%) 2) Reject frequencies below 50Hz (by at least 50 dB) 3) Reject frequencies above 150Hz (by at least 40 dB)
      1. Calculate the center frequency and sketch the filter requirements
      2. Calculate the ideal filter hideal[n].
      3. Choose a window w[n] to meet the requirements (use Slide 22.14).
      4. What is the FIR filter hBP[n]? What is the delay (in ms) of this filter?
      5. To implement this filter as an FIR convolution, how many multiplies and additions are required per output sample.
      6. (not for quiz) Assuming additions take 1 clock cycle, and multiplies take 10, what is the slowest clock speed DSP that can be used for this application using convolution?
      7. (not for quiz) To implement this filter using FFT block processing, calculate how many multiplies and additions are required per output sample for N= 2048.
      8. (not for quiz) What is the slowest clock speed DSP that can be used for this application using the FFT and DSP block processing, using N=2048?
      Nov. 6 (LAB1O)
    Nov. 8 (LAB2O)
    Nov. 12 (LAB1E)
     

    5b   We wish to implement a band-pass filter to demodulate an AM radio station with frequency content in the range 726−734kHz (content in this range should be accepted ±1%). We need to reject frequencies below 720kHz and above 740kHz by at least 40dB. We use a A/D system with a sampling frequency of 2MSamples/sec. Our DSP takes 1 clk cycle for addition and 5 clk cycles for (complex) multiplication (assume other operations are zero cost).
    1. Sketch the filter specifications. What are ωp,L, ωp,H and ωs,L, ωs,H?
    2. Calculate ωc, ω0 for the BPF. Calculate the ideal BPF.
    3. Choose a windowing function and window length for this filter.
    4. Calculate the expression for the FIR filter to implement this specification.
    5. To implement this filter as an FIR convolution, how many multiplies and additions are required per output sample.
    6. What is the slowest clock speed DSP that can be used for this application using FIR convolution?
    7. To implement this filter using FFT block processing, calculate how many multiplies and additions are required per output sample, for N= 4096
    8. What is the processing delay for the FIR?
    Consider a filter described by H(z) = Y(z)/X(z), where
    H(z) = 2z−2/(1 − z−1 − 2z−2)
    1. Given samples of x[n] = {1,2,3,4}, calculate the output y[n] for the filter Assume zero initial conditions.
    2. Factorize H(z) into a form
      H(z) = Az−2/(1 − az−1) + Bz−2/(1 − bz−1)
    3. Calculate the inverse z-transform h[n].
      Nov. 20 (LAB1O)
    Nov. 22 (LAB2O)
    Nov. 26 (LAB1E)
     

    Laboratories

    Lab attendance is a compulsory component of this course. Laboratories will be three hours alternate weeks as per the registration schedule. Attendance is compulsory. Labs will consist of programming in MATLABtm, developing filter models in SIMULINKtm, and using the TI TMS320C6713 DSP starter kit board.

    Students must do labs in groups of two. Lab results must be shown to T.A. before the end of the lab period.
     
    No.  Laboratory  Lab Date 
    1   Lab #1, Filter model for lab.   Sep. 11 (LAB1O) Sep. 13 (LAB2O) Sep. 17 (LAB1E)  

    2   Lab #2,
    Sheet music and mat file with notes for "Country Gardens"
    Instructions to bypass speakers
      Sep. 25 (LAB1O) Sep. 27 (LAB2O) Oct. 1 (LAB1E)  

    3   Lab #3, DSP Software   Oct. 9 (LAB1O) Oct. 11 (LAB2O) Oct. 15 (LAB1E)  

    4   Lab #4 (updated)
    You'll also need Lab4 sound files
      Oct. 23 (LAB1O) Oct. 25 (LAB2O) Oct. 29 (LAB1E)  

    5a   Lab #5 (updated Nov. 6)
    Note: Code samples will be posted monday, Nov. 6
    You'll also need Lab5 sound files and Lab5 DSP code
      Nov. 6 (LAB1O) Nov. 8 (LAB2O) Nov. 12 (LAB1E)  

    5b   Continuation of lab 5a (Update: No new questions for lab #5b)   Nov. 20 (LAB1O) Nov. 22 (LAB2O) Nov. 26 (LAB1E)  

    Course Outline

    Date   Activity  
    Sep. 10, Sep. 12   Introduction to DSP: Slides #0, Slides #1,
    Matlab Programming for DSP: Slides #5,
    Quantization: Slides #13,
    The Loudness War [Youtube],
     
    Sep. 17, Sep. 19   Signals and Systems
    Slides #2, Slides #3, Slides #4
    Sound&Wave[Youtube], Sonata Pathétique[Youtube]
    Sep. 19: Guest Lecture: Mako Hirotani: Notes, PRAAT Software
     
    Sep. 24, Sep. 26   Fourier Analysis
    Slides #6, Slides #7, Slides #8, Slides #9, Slides #23,
    DSP Examples: Example #1, Spectrogram View[Youtube],
     
    Oct. 1, Oct. 3   Sampling
    Slides #10, Slides #11, Slides #12,
    Antialiasing fonts: Sub-pixel rendering, Anti-aliasing
    DSP Examples:
     
    Oct. 8   Class cancelled (Thanksgiving day)
     
    Oct. 10, Oct. 15   Discrete Fourier Transform,
    Slides #14, Slides #15, Slides #16, Slides #17,
     
    Oct. 17   Review:
    Midterm Review (2011) Practice Midterm (F08), Midterm (+ solutions), Midterm exam 2008, Midterm exam 2007 (with solutions − remove t in solution for Q#1),
     
    Oct. 22   Midterm exam #1
     
    Oct. 24, Oct. 29, Oct. 31   FIR Filter Design
    Slides #18, Slides #19, Slides #20, Slides #21, Slides #22,
     
    Nov. 5, Nov. 7, Nov. 12   Spectrogram, Fast Fourier Transform
    Slides #23, Slides #24, Slides #25,
     
    Nov. 14   Review
     
    Nov. 19   Midterm exam #2: Material is 2−12,14−25
    Location: SA306
     
    Nov. 12, Nov. 21, Nov. 26, Nov. 28   Z-Transform, Transform analysis of systems, Advanced topics
    Slides #28, Slides #29, Slides #30, Slides #31, Slides #32, Slides #33,
     
    Dec. 3   Review,
     
    Dec. 12   Final Exam, 9:00−11:30 (AT 301)
     

    Code Examples

    Code examples given in class are listed here:
    Date   Code  
    Sep. 12  
    time = 0:300; signal1 = zeros(1,100); signal2 = linspace(4000,800,101); signal = [signal1, signal2, signal1]; plot(time,signal,'k'); hold on; ylim([-1000,5000]); sample_time = (0:6)*50 + 1; thresh = -3500+1000*(0:6); for i=1:length(sample_time) stime_i = sample_time(i); samp_i = signal(stime_i); stem(stime_i, samp_i,'b'); gt_thresh = samp_i > thresh; adcvalue = sum( gt_thresh); repvalue = (adcvalue-4)*1000; stem(stime_i,repvalue,'r') fprintf('%4d ',[i,samp_i, adcvalue,repvalue]);fprintf('\n'); end hold off

     
    Sep. 25   Music from Brad Sucks. Full song is available under Creative Commons license as Making Me Nervous. (Aside, the artist has a new record release, if you're interested: Brad Sucks Record Release @ Zaphods November 2, 2012 - Ottawa, ON )

    Step #1: Download sample: Sample (10.5s−18.5s)

    [y,fs] = wavread('Brad_Sucks_-_Making_Me_Nervous_10s-18s.wav'); time = (0:length(y)-1)/fs; ch1 = y(:,1)/2; ch2 = y(:,2)/2; for r = [2,1,0.5]; out1= ch1 * r; subplot(211); plot(time,out1); ylim([-1,1]); out2= ch2 / r; subplot(212); plot(time,out2); ylim([-1,1]); pause wavwrite([out1,out2],fs, ['Amplitude-',num2str(r),'.wav']); end
    Output: Amplitude-0.5.wav, Amplitude-1.wav, Amplitude-2.wav
    [y,fs] = wavread('Brad_Sucks_-_Making_Me_Nervous_10s-18s.wav'); for D = [50,100,300,1000,1e4]; delay = zeros(D,1); out1 = [ch1; delay]; out2 = [delay; ch2]; wavwrite([out1,out2],fs, ['Delay-',num2str(D),'.wav']); out1 = [delay; ch1]; out2 = [ch2; delay]; wavwrite([out1,out2],fs, ['Delay+',num2str(D),'.wav']); end
    Output: Delay+50.wav, Delay+100.wav, Delay+300.wav, Delay+1000.wav, Delay+10000.wav, Delay-0.5.wav, Delay-0.wav, Delay-50.wav, Delay-100.wav, Delay-300.wav, Delay-1000.wav, Delay-10000.wav,
     
    Oct. 1   Samples from Slides #23,
    fs=8192; t=0:1/fs:0.2; x1=[]; notes=[3 5 7 8 10 12 14 15]; for i=notes; x1=[x1 cos(2*pi*(220*2^(i/12))*t)]; end; X1=fft([zeros(1,1000) x1 zeros(1,1000)]); W=linspace(0, fs, length(X1)); subplot(211); plot(W,abs(X1)); xlim([1,1000]); subplot(223); specgram(x1,64,fs); ylim([0,1500]); subplot(224); specgram(x1,2048,fs); ylim([0,1500]); print slides23-sound1.png wavwrite(x1*.99,fs,16,'slides23-sound1.wav')
    Output: slides23-sound1.png, slides23-sound1.wav
    x2=zeros(1,length(t)); for i=notes; x2=x2+cos(2*pi*(220*2^(i/12))*t); end; X2=fft([zeros(1,1000) x2 zeros(1,1000)]); W=linspace(0, fs, length(X2)); specgram(x2,64,fs) subplot(211); plot(W,abs(X2)); xlim([1,1000]); subplot(223); specgram(x2,64,fs); ylim([0,1500]); subplot(224); specgram(x2,2048,fs); ylim([0,1500]); print slides23-sound2.png wavwrite(x2*.99,fs,16,'slides23-sound2.wav')
    Output: slides23-sound2.png, slides23-sound2.wav
     
    Oct. 10   Detecting onset time and BP filtering: Original Signal
    [y,fs] = wavread('Brad_Sucks_-_Making_Me_Nervous_10s-18s.wav'); x=y(1:175e3,:); t= (1:175e3)/fs; subplot(411); plot(t,x); set(gca,'XTickLabels',[]); title 'Original Signal (Blue,Red = Audio Channels)' Wbp= [120 140]/(fs/2); %NOT HOW WE DEFINE w IN COURSE [b,a] = cheby1(2,0.2,Wbp); y1= filter(b,a,x); subplot(412); plot(t,y1); set(gca,'XTickLabels',[]); title 'BP Filter [120,140]' Wbp= [180 200]/(fs/2); [b,a] = cheby1(2,0.2,Wbp); y2= filter(b,a,x); subplot(413); plot(t,y2); set(gca,'XTickLabels',[]); title 'BP Filter [180,200]' z= abs(y2(:,1)); zf = filter(.001,[1,-.999],z); zt = 0.2*(zf>.1); subplot(414); plot(t,[z,zf,zt]); title 'Onset time'
    Output: Output Image
     
    Oct. 24   Detecting signal amplitude Original Signal
    [y,fs] = wavread('Brad_Sucks_-_Making_Me_Nervous_10s-18s.wav'); x=y(1:175e3,:); t= (1:175e3)/fs; subplot(311); plot(t,x); set(gca,'XTickLabels',[]); title 'Original Signal (Blue,Red = Audio Channels)' z= abs(y2(:,1)); zf = filter(.001,[1,-.999],z); %SCHMITT TRIGGER thresh = 0.1; for i=1:length(zf) if zf(i) > thresh; thresh = 0.09; zt(i) = 1;end if zf(i) < thresh; thresh = 0.11; zt(i) = 0;end end subplot(312); plot(t,[z,zf,0.2*zt]); title 'Onset time' startpts = find( diff(zt)>0 ); endpts = find( diff(zt)<0 ); hold on; plot(t(startpts),0.32,'k+'); plot(t(endpts),0.32,'ko'); hold off; zs = filter(1,[1,-1],z); subplot(313); plot(t,[zs.*zt]); title 'Amplitude' for i=1:length(startpts) delta = zs(endpts(i)) - zs(startpts(i)); text(t(startpts(i)), zs(endpts(i)), sprintf('%5.1f',delta)); end
    Output: Output Image
     
    Oct. 31   Bandpass filter Design
    [y,Fs] = wavread('Brad_Sucks_-_Making_Me_Nervous_10s-18s.wav'); x=y(1:175e3,1); t= (1:175e3)/Fs; F0 = 200; f0 = F0/Fs; Fc = 20; fc = Fc/Fs; TBW = .001; %Require 50dB, use Hamming L = ceil(1.90/TBW); W = hamming(2*L+1); n=(-L:L)'; h_BP = 2*fc*sinc(2*fc*n) .* (2*cos(2*pi*f0*n)); subplot(311); plot(n+L,h_BP,'k',n+L,h_BP.*W,'b'); xlim([0,2*L]); subplot(312); semilogy(linspace(0,Fs,2*L+1),abs(fft([h_BP,h_BP.*W]))); xlim([0,500]); ylim([1e-4,1]); subplot(313); plot(t,[x,3*filter(h_BP.*W,1,x)]);
    Output: Output Image
     
    Nov. 5   Spectrogram
    [y,Fs] = wavread('Brad_Sucks_-_Making_Me_Nervous_10s-18s.wav'); x=y(1:175e3,1); t= (1:175e3)/Fs; clf axes('position',[0.04,0.68,0.92,0.28]); specgram(x,64,Fs); xlabel(''); set(gca,'Xticklabel',[]); ylabel('N=64'); set(gca,'Yticklabel',[]); ylim([0,5e3]); axes('position',[0.04,0.38,0.92,0.28]); specgram(x,512,Fs); xlabel(''); set(gca,'Xticklabel',[]); ylabel('N=512'); set(gca,'Yticklabel',[]); ylim([0,5e3]); axes('position',[0.04,0.08,0.92,0.28]); specgram(x,4096,Fs); ylabel('N=4096'); set(gca,'Yticklabel',[]); ylim([0,5e3]); xlabel('Frequency (0-5kHz) vs Time (s)');
    Output: Output Image
     
    Nov. 26   BPF and z-plane zeros
    Fs = 44100; Fs = Fs/20; % Scale Fs (otherwise too many to view) F0 = 200; f0 = F0/Fs; Fc = 20; fc = Fc/Fs; TBW = .02; %Require 50dB, use Hamming L = ceil(1.90/TBW); W = hamming(2*L+1); n=(-L:L)'; h_BP = 2*fc*sinc(2*fc*n) .* (2*cos(2*pi*f0*n)); h_BP_W = h_BP.*W; subplot(311); plot(n+L,h_BP,'k',n+L,h_BP_W,'b'); xlim([0,2*L]); title 'BPF windowed (blue) original (black)' subplot(323); hh=zplane(h_BP', [1,zeros(1,2*L)]); set(hh,'Color',[0,0,0]); axis(1.1*[-1,1,-1,1]); axis normal subplot(324); hh=zplane(h_BP', [1,zeros(1,2*L)]); set(hh,'Color',[0,0,0]); axis([0.65,1.0,.3,.75]); axis normal subplot(325); zplane(h_BP_W', [1,zeros(1,2*L)]); axis(1.1*[-1,1,-1,1]); axis normal subplot(326); zplane(h_BP_W', [1,zeros(1,2*L)]); axis([0.65,1.0,.3,.75]); axis normal

      Output: Output Image
     
    Nov. 27   Distortion effects
    Common code to all distortion examples
    [y,Fs] = wavread('Brad_Sucks_-_Making_Me_Nervous_10s-18s.wav'); ch1 = y(:,1)/2; ch2 = y(:,2)/2; time = (0:length(y)-1)/Fs;
    original
     
    Increase Stereo separation
    % Increase stereo separation chm = 0.5*[ch1+ch2]; chd = 0.5*[ch1 - ch2]; for sep = [0,1,2,4] out1 = chm + sep*chd; out2 = chm - sep*chd; fname = sprintf('stereo-sep%3.1f.wav',sep); wavwrite([out1,out2],Fs, fname); end
    Output: original, stereo-sep0.0.wav, stereo-sep1.0.wav, stereo-sep2.0.wav, stereo-sep4.0.wav,
     
    Adding reverb of different lengths
    % reverb for rev_len = [1000,3000,10000]; fir = [1,zeros(1,rev_len-1)]; RN = 20; fir(ceil(rev_len*rand(1,RN))) = 0.5*randn(1,RN); out1 = filter(fir,1,ch1)/2; out2 = filter(fir,1,ch2)/2; fname = sprintf('reverb-samp%4d.wav',rev_len); wavwrite([out1,out2],Fs, fname); end
    Output: original, reverb-samp1000.wav, reverb-samp3000.wav, reverb-samp10000.wav,
     
    Non-linear distortion
    cha = 0.5*[ch1+ch2]; for distfac=[200,500]; chf = cha*distfac; out = atan(chf); out = out/max(abs(out))*lim_chf; % set to original amplitude out = out + chr; % add in other frequencies fname = sprintf('nonlin=%3.1f.wav',distfac); wavwrite(out,Fs, fname); end
    Output: original, nonlin=200.0.wav, nonlin=500.0.wav
     
    Non-linear distortion in a Band-Pass filtered region.
    F0 = 200; f0 = F0/Fs; Fc = 50; fc = Fc/Fs; TBW = .02; %Require 50dB, use Hamming L = ceil(1.90/TBW); W = hamming(2*L+1); n=(-L:L)'; h_BP = 2*fc*sinc(2*fc*n) .* (2*cos(2*pi*f0*n)); h_BP_W = h_BP.*W; h_BS = (n==0) - h_BP_W; chf = filter(h_BP_W,1,cha); lim_chf = max(abs(chf)); chr = filter(h_BS ,1,cha); for distfac=[200,500]; chf = chf*distfac; out = atan(chf); out = out/max(abs(out))*lim_chf; % set to original amplitude out = out + chr; % add in other frequencies fname = sprintf('nonlin-cf=%3.1f.wav',distfac); wavwrite(out,Fs, fname); end
    Output: original, nonlin-cf=200.0.wav, nonlin-cf=500.0.wav
     

    Last Updated: $Date: 2013-09-23 14:04:49 -0400 (Mon, 23 Sep 2013) $