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Assume you do a polyphase decomposition into $M$ shorter filters, because that's really the best you can do in exploiting the decimation properties of your system. Your $M$ shorter filters are just that: FIR filters. You can then go ahead and take these filters and decompose it into $c=\left\lfloor\frac KM\right\rfloor$ filters each. That way, you get $cM$ ...


3

The short answer is the polyphase filter converts a low pass filter into a series of all pass filters each with a different time delay. So it is a series of delays at even fractions of the time between samples of the lower sampling rate of the polyphase filter. By getting an output of the same signal at different fractional delays, we can combine these to ...


3

Answer: You will see residual images of $X(f)$ at multiples $f_s$, $2f_s$ and $3f_s$, and distorted image of $X(f)$ at non-zero multiples of $4f_s$, when sampling in the manner you explained. Depending on value $e$, the size of residual will change. I have explained how in detail below. Ideally, sampling at $4f_s$ would have completely cancelled those ...


1

To start with, XAPP1161's developers re-use, for their transmitter and receiver blocks, the objects dsp.ChannelSynthesis and dsp.Channelizer, respectively. These are objects of MATLAB's DSP System Toolbox. The Channel Synthesizer block diagram corresponds to the transmitter block in XAPP1161's Figure 3 Polyphase Filter Bank (page 3), and the Channelizer ...


1

A polyphase channelizer is not a special kind of filter. It is a structure that works well when using filters in multi rate settings. Polyphase is a sampling rate conversion method that leads to efficient implementations that are useful for building filter banks. The efficiency comes from only having to design one filter. The downside is that the extracted ...


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