19-01-2013, 02:55 PM
Digital Filter Banks
Digital Filter.ppt (Size: 290 KB / Downloads: 201)
The digital filter bank is set of bandpass filters with either a common input or a summed output
An M-band analysis filter bank is shown below
The subfilters in the analysis filter bank are known as analysis filters
The analysis filter bank is used to decompose the input signal x[n] into a set of subband signals with each subband signal occupying a portion of the original frequency band
The subfilters in the synthesis filter bank are known as synthesis filters
The synthesis filter bank is used to combine a set of subband signals (typically belonging to contiguous frequency bands) into one signal y[n] at its output
Uniform Digital Filter Banks
A simple technique to design a class of filter banks with equal passband widths is outlined next
Let represent a causal lowpass digital filter with a real impulse response :
The filter is assumed to be an IIR filter without any loss of generality
Uniform DFT Filter Banks
The computational complexity of an M-band uniform DFT filter bank is much smaller than that of a direct implementation as shown below
For example, an M-band uniform DFT analysis filter bank based on an N-tap prototype lowpass filter requires a total of multipliers
On the other hand, a direct implementation requires NM multipliers
Nyquist Filters
Under certain conditions, a lowpass filter can be designed to have a number of zero-valued coefficients
When used as interpolation filters these filters preserve the nonzero samples of the up-sampler output at the interpolator output
Moreover, due to the presence of these zero-valued coefficients, these filters are computationally more efficient than other lowpass filters of same order
Half-Band Filters
Attractive property: About 50% of the coefficients of h[n] are zero
This reduces the number of multiplications required in its implementation significantly
For example, if N = 101, an arbitrary Type 1 FIR transfer function requires about 50 multipliers, whereas, a Type 1 half-band filter requires only about 25 multipliers