08-12-2012, 02:42 PM
Multirate Signal Processing
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In this exercise we will study multirate digital signal processing and filterbanks using Matlab. For
completing this work you have to study Parts IV and V of the lecture notes for the course SGN-
2106 Multirate Signal Processing (Part I and II might be also needed to understand the basics of
multirate systems in the case you are not familiar with multirate systems). Part IV can be found on
the shelf in front of TC403. First third (other two thirds are not needed for this work) of Part V can
be downloaded from http://www.cs.tut.fi/~bregovic/multi51.pdf.
Additional reading material on the topics considered in this laboratory work can be found in the
book “Digital Signal Processing, a Practical Approach” [1]. More about filter design related to this
work can be found in [2] with filterbanks described in more detail in [3].
The student should have some background in multirate signal processing. Working experience with
Matlab is highly recommended.
Design of Multirate FIR Filter
Narrow-band linear-phase finite-impulse-response (FIR) filters can be efficiently implemented
using multirate technique. In this technique, the sampling frequency is first decreased and the actual
FIR filter is implemented at the lower sampling frequency. This considerably reduces the
complexity of the filter. After filtering the sampling frequency is increased back to the desired level.
Next we compare two FIR filter designs which have the same specifications. The first one is a
normal FIR filter and the second one is a multirate FIR filter.
FIR filter design
Design a linear-phase FIR filter using minimax approximation (equiripple in the passband and
stopband). This can be done using firpm function in Matlab (or remez in some older versions of
Matlab) and the filter order can be estimated by using firpmord function (remezord in some
older versions of Matlab). The filter specifications are as follows:
• passband edge p = 0.01 fs/2
• stopband edge s = 0.0105 fs/2
• passband ripple p 0.02 (0.35-dB passband ripple)
• stopband ripple s 0.00316 (50-dB stopband attenuation).
What is the minimum order of a linear-phase FIR filter to meet the above specifications? How many
multiplications per output sample are required if the coefficient symmetry is utilized? (It is not
necessary to calculate the filter coefficients.)
FIR filter design using multirate technique
Design an FIR filter using multirate technique (see Figure 1). The overall structure in Figure 1
should meet the same specifications which are given above. You should decrease the overall
sampling rate as much as possible because the complexity of the filter H(z) depends on the sampling
rate fs / (MN). When you have chosen the overall sampling rate reduction, implement the sampling
rate conversion using two decimation/interpolation stages (M and N). It is not necessary to go
through all the possible combinations of the decimation factors M and N but chose some reasonable
partition.
Design of Two-Channel Orthogonal Filterbank
Next we will study filterbanks where the interpolation and decimation is utilized. Figure 2 shows a
simple two-channel filterbank. Analysis bank [H0(z) and H1(z)] divides the input signal x[n] in two
frequency bands ([0, fs / 4] and [fs / 4, fs / 2]), resulting in subband signals x0[n] and x1[n]. The
synthesis bank [F0(z) and F1(z)] combines the subband signals into the output signal y[n].