Assignments

• Assignment 1 (due Tuesday January 14, 2020):
  1. Read Smith and Jaffe's paper found here.
  2. Implement a parametric circular delay line in Matlab, where the single parameter $M$ is the integer length of the effective delay.
     • your delayline should accommodate a number of integer delay values (this is the parameter) using a single delayline;
     • implement the integer sample delay using a read and write pointer to a delay line having a length that's set according to the longest expected delay (lowest frequency);
     • to make sure you implemented correctly, check its impulse response: the output in response to an impulse as input.

  3. Use your delay line to create a feedforward comb filter with gain coefficient $g$.
     • how does your output compare to the output of Matlab's filter function?

       Matlab M-sample delay feedforward comb filter
       
       M = ...;               % sample delayn
       g = ...;               % comb filter coefficient
       N = ...;               % signal length
       x = [1; zeros(N-1,1)]; % input impulse
       
       filter([1; zeros(M-1); g], 1, x);
       

  Solutions:

  • cdl.m
  • cdlffcomb.m

• Assignment 2 (due Tuesday January 21, 2020):

  Beginning with your circular delay line:

  1. implement fractional delay using linear interpolation
  2. implement a flanger with a variable length delay that oscillates between some maximum and minimum value (with linear interpolation for fractional delay).
  3. implement a chorus effect with a multi-tap delay line.
  4. implement a feedback comb filter with feedback coefficient $g$

  Solutions:

  • flanger.m (flanger with linear interpolation)

• Assignment 3 (due Tuesday January 28, 2020):

  Beginning with your (non-interpolating) circular delay line:

  • implement a feedback comp filter, setting feedback coefficient $g$ given note duration (T60) and integer sample delay $M$.
  • implement the karplus strong for an integer delay using a noise burst for excitation and the simple lowpass filter in the feedback loop.

  Solutions:

  • karplus.m (simple Karplus-Strong string, with integer delay)

• Assignment 4 (due Tuesday February 4, 2020):

  Beginning with your Karplus-Strong pluck string model, extend using

  • allpass fraction delay for tuning
  • decay length (note duration) shortening for low frequencies
  • BONUS: decay length stretching so you can specify a note duration (this will create a change in the phase delay of the lowpass filter and the overall loop duration and sounding frequency).

• Assignment 5 (due Tuesday Febrary 18, 2020):

  Implement a 1-D digital waveguide (bi-directional delay line) of a plucked string.

  • Use your non-interpolating delay line to create your wavegude structure: begin with inversions but no losses at each end.
  • Check 1: Input and impulse at one end. If tapped at the same location as the input, the impulse response should be a sequence of 1s seperated by N-1 zeros (where N is the round-trip delay, and N/2 is the delay for each delay line).
  • Check 2: make sure the sum of right and left traveling waves is always zero at the boundaries.
  • Add lowpass filter. Is it beginning to sound string like?
  • Choose a plucking position and initialize the string to a triangle shape (as shown in class and in notes).
  • Choose a pickup point and sum upper and lower delaylines at that point to produce the output waveform. Listen!

• Assignment 6 (due Tuesday February 25, 2020): Implement a sequence of N 2-port scattering junctions and use it to model the human vocal tract when vocalizing any of the following vowel sounds:
  • 3-bird
  • A-bart
  • ae-bat
  • E-bet
  • i-beet
  • I-bit
  • O-ball
  • u-food
  • U-foot
  • V-but
  where each linked file is a sequence of cross-sectional areas.
  1. BEFORE using the files, test with a simple vector of cross-sectional areas that are all the same,

     S = [1 1 1 1];
     Nj = length(S) - 1;
     k = (S(1:end-1) - S(2:end)) ./ (S(1:end-1) + S(2:end));
     

     as this should produce the same output as a purely cylindrical waveguide model.
  2. LOAD files into Matlab:

     load 'A-bart44100.txt';
     

     Try your model with the following source as input:
     • source.wav