IIR filter in DSP

1. IIR is an acronym for Infinite Impulse Response.

2. In this filter, the output is fed back to the input of the filter, thus creating a recursive action, hence, this filter is also known as recursive digital filters.

3. If we give an impulse as an input to the filter, then infinite number of non-zero values are seen at the output. This is also credited to the concept of feedback used in this filter.

4. The frequency response of IIR filter is exceptionally good but the phase characteristics are not linear. Due to this, these filters can be used in those applications where frequency response is of prior interest and phase considerations are not desired or taken into account.

5. The filter order, n, determines the number of input and output samples required to be saved for the computation of next output sample. (n input samples+ n output samples+ current sample= 2n+1 samples are required to be saved).

6. The transfer function is a polynomial expressed in the terms of (z-1). The values of z for which transfer function is zero correspond to zeroes of the transfer function and the values of z for which the transfer function approaches to infinity correspond to poles.

7. At w, phase shift of zero is seen at the output but at 3w phase shift of 180 deg occurs at the output. This indicates that phase response between input and output is non-linear.

8. Due to the employment of feedback, a problem of potential instability is often encountered in these filters. This has to be taken care of while designing the filter.

9. The applications of IIR include:

- In image edge detection and enhancement
- The FPGA based IIR filters are finding their usage in Digital Television Technology
- In applications where amplitude is of only interest
- In high speed and low power communication transceivers
- In audio signal processing technology like speakers and for sound processing function
- In CPU
- For notching and band limiting
- For noise-shaping
- As itis inexpensive to design, it can be used in designing low-cost signal processors.