![]() 12 7.2 Multirate implementation of IFIR design. 3.2.3 A word on practical implementation 2Īdvanced design algorithms - interpolated FIR lters 10 7.1 Further IFIR optimizations. 3.2.2 More general nonlinear-phase designs. Optimal FIR designs with xed transition width and lter order 3.1 Linear-phase designs. Ĭontents1 2 Ideal lowpass lter FIR lowpass lters 2.1 FIR lter design specications. Other equiripple designs 6.1 Constrained-band equiripple designs. Optimal equiripple designs with xed peak ripple and lter order 5.1 Minimum-phase designs with xed peak ripple and lter order. Optimal equiripple designs with xed transition width and peak passband/stopband ripple 4.1 Minimum-phase designs with xed transition width and peak passband/stopband ripple. The theory behind the design algorithms is avoided except when needed to motivate them. The tutorial focuses on practical aspects of lter design and implementation, and on the advantages and disadvantages of the different design algorithms. The emphasis is mostly on lowpass lters, but many of the results apply to other lter types as well. Natick, MA 01760, USAĪbstractThis tutorial white-paper illustrates practical aspects of FIR lter design and xed-point implementation along with the algorithms available in the Filter Design Toolbox and the Signal Processing Toolbox for this purpose. If unspecified, it defaults to 80 dB.Practical FIR Filter Design in MATLAB RRevision 1.1 The amount of attenuation can be set to any desired value for both interpolation and decimation. For decimation, the filter passes about half of the band, that is 0 to Fs/4, and attenuates the other half in order to minimize aliasing. ![]() In the case of interpolation, the filter retains most of the spectrum from 0 to Fs/2 while attenuating spectral images. Visualize the magnitude response using fvtool. These system objects can also work with custom sample rates. The IIR counterparts dsp.IIRHalfbandInterpolator and dsp.IIRHalfbandDecimator can be even more efficient. These system object are implemented using an efficient polyphase structure specific for that rate conversion. The dsp.FIRHalfbandInterpolator and dsp.FIRHalfbandDecimator objects perform interpolation and decimation by a factor of 2 using halfband filters. ), you can perform sample rate conversion by a factor of 2. The Special Case of Rate Conversion by 2: Halfband Interpolators and Decimators An FIR decimator can be implemented as follows. Filtered Rate Conversion: Decimators, Interpolators, and Rational Rate Convertersįiltered rate conversions includes decimators, interpolators, and rational rate converters, all of which are cascades of rate change blocks with filters in various configuations.įiltered Rate Conversion using the filter, upsample, and downsample functionsĭecimation refers to LTI filtering followed by uniform downsampling. The next few sections show the use of these functions to design the filter and demonstrate why designMultirateFIR is the preferred way. fir1, firpm, or fdesign) could design an appropriate anti-aliasing and anti-imaging filter, the function designMultirateFIR gives a convenient and a simplified interface. While any lowpass FIR design function (e.g. This filter is a lowpass with the normalized cutoff frequency of and a gain of. A single filter that combines anti-aliasing and anti-imaging is placed between the upsampling and the downsampling stages. The order of rate conversion operation cannot be commuted. This is obtained by upsampling by rate followed by filtering, then downsampling by rate. The combination of upsampling a signal by a factor of, followed by filtering, and then downsampling by a factor of converts the sequence sample rate by a rational factor of. The only difference is in the required gain and the placement of the filter (before or after rate conversion). īoth upsampling and downsampling operations of rate require a lowpass filter with a normalized cutoff frequency of. Ideally, the cutoff frequency of this anti-imaging filter is (like its antialiasing counterpart), while its gain is. The filter removes the spectral images of the low-rate signal. When upsampling by a rate of, a lowpass filter applied after upsampling is known as an anti-imaging filter. Note: the underlying sampling frequency is insignificant, we assume normalized frequencies (i.e. Ideally, such an anti-aliasing filter has a unit gain and a cutoff frequency of, here is the Nyquist frequency of the signal. ![]() This is similar to an analog LPF used in A/D converters. When downsampling by a rate of, a lowpass filter applied prior to downsampling limits the input bandwidth, and thus eliminating spectrum aliasing.
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