22-06-2012, 05:19 PM
Modified Linear Phase Frequency Response Masking FIR Filter
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Introduction
FIR filters designed using conventional methods have
high orders for sharp transition filters, which renders real
time high speed implementation impractical. Several
methods have been proposed in the literature for reducing
the complexity of sharp FIR filters [1]. One of the most
successful techniques for synthesis of very narrow
transition width filters is the frequency response masking
technique because of reduced arithmetic complexity
involved [2]-[4]. The major advantages of the frequency
response masking approach is that it employs subfilters
with very sparse coefficient vector and its resulting filter
has a very sparse coefficient vector. These filters are
suitable for VLSI implementation since hardware
complexity is reduced.
Frequency Response Masking Approach
In the frequency response masking technique [2] the
overall filter is composed of several sub-filters. The first
subfilter is known as model filter which is upsampled to
form the sharp edge needed in a narrow transition width
filter. The second subfilter is the complement of the model
filter, which is used to form the arbitrary bandwidth of the
overall filter response. The other two subfilters are
masking filters which extract one or several passbands of
the periodic model filter and periodic complementary
model filter and remove unwanted frequency components
to form the stop band of the overall filter response.
Bandpass Subfilter Design
In our approach, the design is adaptable to any change
in the center frequency and passband width of the desired
bandpass filter and is a direct design involving a single
filter. The approximate response of the bandpass filter is
formulated for equiripple passband, sharp transition,
arbitrary center frequency and passband width.
Conclusions
We have proposed a novel technique for a linear phase,
sharp transition, low arithmetic complexity lowpass FIR
filter obtained by modifying the Frequency Response
Masking approach. Our subfilter design is simple, without
optimizations and only one masking filter need to be
designed instead of the two masking filters required in [2].
The bandpass filter has wider transition response which
reduces arithmetic complexity of the subfilter. Various
regions of the subfilters are approximated with
trigonometric functions of frequency, making it
convenient to evaluate the impulse response coefficients in
closed form. Unlike in Frequency Response Masking
approach, the transfer function for subfilters in our
approach is evolved in frequency and time domain. The
accuracy of the filter approximation can be improved by
including a larger number of terms in the impulse response
sequence. The lowpass realization can be extended to the
realization highpass, bandstop and bandpass filters with
arbitrary bandwidths & center frequencies.