Here is some guitar sound to use as test input, and also some speech sound.
Implement the bandpass filter with configurable \(f_c\) and \(f_d\).
Implement a three-way equalizer by first splitting the input signal with a low- and a high-pass filter with the same cut-off frequency, and then splitting the high-pass signal again in the same way. Multiply each channel by some (maybe time-varying) factor and add them back together. Check (and maybe proof) whether the input signal would be unchanged if the factors are all equal to 1.
Implement a phaser with only one allpass. Modulate \(f_c\) with a low-frequency oscillator.
Extend the phaser to four allpasses with separate parameters for each allpass. Modulate the \(f_c\)-parameters independently with non-harmonic low-frequencies. Also try to implement the feedback loop. The result should sound like this.
Implement a 4-fold Wah-Wah effect. Modulate \(f_c\) with a low-frequency oscillator, and calculate \(f_d\) in a constant-q manner. The result should sound like this.
Generate a 5 second sine tone and resample it to an almost similar sampling rate using linear, Lanczos and allpass-interpolation. See if you can hear any difference for high frequencies. (Test with a low sampling frequency.)
Implement a stereo rotary speaker effect. The result should sound like this.
Implement a compressor that uses a squarer as detector and limits the level at -30dB. To test it, read guit3.wav and fox.wav, and mix them together with guit3.wav divided by 10 (radio host situation). Experiment with attack- and release-time parameters. The result should sound like this.
Some caveats: (1) The output of the squarer is converted to dB by 10*log_{10} because it is squared, otherwise it is 20*log_{10}. (2) For the second averager, the role of attack and release are reversed.
Implement the distortion transforms from the lecture notes (hard clipping, soft clipping, distortion), and test them on the guitar sound.
Implement the vocoder effect (mutation, morphing) based on STFT. You can use the following files: stft.m, istft.m.
Implement time-stretching based on STFT.
Implement an oscillator according to the digital resonator. Control the frequency with an LFO (low frequency oscillator). For large and fast frequency variations there should be audible amplitude variations. Now determine the amplitude by a squarer-detector and an averager (equal attack and release). Correct the amplitude by dividing \(x[t]\) and \(x[t-1]\) by \((a-\bar{a})/10+1\), where \(a\) is the detected amplitude and \(\bar{a}\) is the desired expected amplitude.
No MatLab this time. For the signal $$x=(\ldots,0,0,1,2,1,0,-1,-2,-1,0,0,\ldots)\, ,$$ calculate the optimal linear prediction coefficients with the Levinson-Durbin algorithm by hand. No window function is used, i.e. it is constant 1. \(m\) is as far as we can get in 0.75 hours. Check the result after each step. Calculate the residual signal.
Convolve the input signal with two different white-noise signals (length about 4000 samples) to get a decorrelated stereo output. Test it with our test signals and also white noise as input signal. Play the output followed by a convolved but non-decorrelated (use the same white-noise for left and right) signal to hear the difference.
Implement Moorer's reverberator for a one-dimensional room of 4m length. The sound source is at 1m from one end, and the listener is in the middle of the room. Add the direct sound, two early reflections (one from each end), and one comb filter with a delay according to the mode of the room (there is only one) and no low-pass filtering. Also, no all-pass filter. The speed of sound is 343m/s.