Time-Varying Digital Filters

Overview

Time-varying filters are key components of subtractive synthesis systems. In this project you will explore the implementation of time-varying filters, and discover what must be done to ensure that you can produce a clean signal.

Implement your project in HTML. Please install your presentation in a subdirectory called ‘miniproj7’ in the public area of your AFS account.

Deliverables

Sheet of paper containing the URL to the top level page of your project. Be sure that your HTML project includes the following:

Part 1 – LPF Sweep

Consider the file lpfsweep.m, which shows how to apply a Butterworth lowpass filter with a swept corner frequency to a squarewave. Your task in this first part is to investigate several improvements to this file.

(a)     Display the spectrum of the output and listen to the sound. If the goal is to have a nice clean filter sweep, free of audible clicks, then describe how well the goal is satisfied.

(b)     Try using a smaller block size (e.g., N=100). Evaluate the results of this change by looking at the spectrum, listening to the sound, and looking at the time-domain signal (especially at the transitions between blocks).

(c)     See ‘help filter’ to learn about preserving the filter state between blocks. Try this method with the original value of N. Evaluate your results.

(d)     Try combining the improvements from Steps (b) and (c). Evaluate your results

 Summarize your results – what should be done to ensure that a clean waveform is generated when you have a time-varying filter?

 Part 2 – “Wah-Wah” Effect

A “wah” pedal is a device used by electric guitar players to control the bandwidth of the signal. Design a frequency trajectory for a time-varying digital filter that will emulate the effect of the "wah" pedal, and apply your filter to a short sound clip.

Part 3 – Band-Limited Pulse Generator

Square waves make nice wideband sources, but they often cause problems with aliasing.

(a)     Choose an appropriate sampling frequency and fundamental frequency to demonstrate the aliasing effect for a squarewave signal.

(b)     Implement and investigate (e.g., try several parameter choices) the bandlimited pulse generator described by equation 3-91 (p. 272) of Moore. Show that you can produce wideband signals which are free of aliasing problems.

Include sound files, spectrogram displays, and time-domain plots (e.g., plot a few periods of the signal).