To Do: IIR Delay effect

Section: Filtering

Data

Any sound files (you can use the sounds used for the guitar tuner)

Goal

The IIR filter for delay effect can be implement thanks to the following input-output equation ($e[t]$ is the input, $s[t]$ is the output): $$ s[t] = \alpha e[t] + \beta s[t-D] $$ $\alpha\geq 0$ is the scaling factor, $\beta\geq 0$ the attenuation factor and $D\geq 0$ the time delay.

  • Determine the impulse response of the filter for D=1
  • Provide the Frequency response of the filter
  • Implement the delay effect in the time domain
  • Is this implementation always stable ?
  • Discuss the parameters
  • Compare with the FIR implementation