31-03-2012, 04:08 PM
FIR Filter Design in Matlab
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Digital filters with finite-duration impulse reponse (all-zero, or FIR filters) have both advantages
and disadvantages when compared to infinite-duration impulse response (IIR) filters.
FIR filters have the following primary advantages:
• They can have exactly linear phase.
• They are always stable, even when quantized.
• The design methods are generally linear.
• They can be realized efficiently in hardware.
• The filter startup transients have finite duration.
Linear Phase Filters
A filter whose impulse response is symmetric about its midpoint is called a (generalized)
linear phase filter. For such filters,
• The DFT of the impulse response will be either purely real or purely imaginary.
• The magnitude of the DFT is scaled by the filter’s magnitude response (there is no amplitude
distortion).
• The phase shift of a filtered signal will vary linearly with frequency ! (pure time delay
with no phase distortion).
Window-Based Design
Windowing is a common design method for FIR filters. In this method,
• The ideal frequency response H(f) is sampled.
• The corresponding ideal impulse response h(n) is determined by the inverse Fourier transform.
In general, this response cannot be implemented in a digital filter because it is infinite
and noncausal.
• h(n) is symmetrically truncated (multiplied by a finite, symmetric window) to create a
linear phase finite impulse response.
Windowing and Spectra
When a signal is truncated, high-frequency components are introduced that are visible in
the DFT. By windowing the truncated signal in the time domain, endpoints are assigned a
reduced weight. The effect on the DFT is to reduce the height of the side lobes, but increase
the width of the main lobe.