# Questions tagged [multirate]

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### With regards to multirate processing, what are the benefits of having a 'slower' sampled signal?

With regards to multirate processing, what are the benefits of having a 'slower' sampled signal? Let's say I have a continuous signal $$x(t) = \cos(2\pi\cdot3t) + \cos(2\pi\cdot 7t)$$ and it is ...
270 views

### Use polyphase representation to construct a perfect reconstruction filter bank

I'm posting this question in response to Question about zero-phase filter bank This is a homework question for which I found an answer, but I didn't do it the way I was supposed to. I'm wondering ...
73 views

### How to undo dynamic Doppler effect by software?

I have a signal affected by Doppler effect. In general, the Doppler effect changes the scale of the time and frequency domains. So, to undo this phenomenon, I am using a sampling rate converter. Two ...
624 views

### Splitting the Unit Delay

Please refer to the paper Splitting the Unit Delay - Tools for fractional delay filter design by Laakso, Valimaki et.al. I am not able to visualize how the fractional delay is obtained by resampling ...
113 views

### Advantage of complex filtering in multirate applications

I've seen it mentioned in passing in various papers on signal processing and filter design that complex FOR filters can be more efficient when it comes to multirate applications. However I cannot ...
369 views

### Recovering a signal that was upsampled by non-integer factor

I have a data sequence $G[n]$ that is upsampled at the transmitter of a communication system by a non-integer factor ($1.5$ to be precise). At the receiver, I am supposed to downsample the data and ...
55 views

### Understanding sampling rate conversion

I am a little bit confused about the concept of sampling rate conversion. Consider the following question: Wideband telephony signals are sampled at a sampling frequency fS1 = 16kHz. To process these ...
704 views

### Why do Dyadic filterbanks downsample the high pass signal portions?

I'm currently programming a dyadic filter bank and have a question. I notice in all of the visual representations: (from here (Dyadic Analysis Filter Bank)), the high pass filtered output for each ...
132 views

### Perfect reconstruction: what properties must the analysis LPF satisfy

I have been reading on conjugate quadrature filters (CQF). The linked article explains that, if we have a lowpassfilter $h_0$, we can create a set of filters for a perfect reconstruction filterbank. ...
92 views

### Elementary proof of Fourier domain formula of multidimensional downsampling by $M$

I am trying to prove a well-know formula for the multidimensional downsampling by arbitrary downsampling integer matrix $M$ in $d$-dimensional case. The formula is  \hat{y}(\omega)=\frac{1}{\...
582 views

### What would be the effect of repeating samples in time domain on frequency domain?

Consider the operation of up-sampling a signal n times by repeating each sample n times in the time domain. What would the frequency domain response of the resultant signal be like given the frequency ...
60 views

### How does multi-rate processing work?

In the case with a 1-D input like audio, how can a system with one input do many different kinds of processing at different sampling rates and still, at the end of the processing, produce one waveform?...
56 views

### Drawbacks of upsampling using polynomial interpolation

I've come across an upsampler that uses polynomial interpolation and no filter. What are the drawbacks to this? I looks more efficient than filtering.
37 views

### Reversing the order of up and downsampling

When we are dealing with the problem of changing the sampling rate by a noninteger factor like L/M, we first need to the do the upsampling, and then the downsampling. My question is that under which ...
23 views

### Decimator effect on wide sense stationary input

I've seen that the output of a decimator when a WSS process is passed through remains WSS. I am not able to immediately see why this is. What is a good explanation of why the signal maintains ...
266 views

### Confusion in FFT of Resampled Data

I have the following code in Matlab: ...
288 views

### Polyphase Commutator

I am rather new to the polyphase structure and thought I had understood, but apparently I havent. My question is I guess very simple: what is the commutator at the input of a polyphase decimator? Is ...
120 views

### Polyphase Analysis Filter Bank

I have a question regarding the polyphase DFT filter bank implementation in this page. (https://cnx.org/contents/Peqc-TK2@16/Uniformally-Modulated-DFT-Filterbank) In figure 2, to analyze the kth ...
128 views

### How do multirate systems introduce 'efficiency' in computation?

I've started reading more into multirate systems recently and am somewhat confused. The concepts introduced seem to make sense, that is, how the decimation and interpolation can change certain ...
19 views

### Converting the equalizer coefficients from VSA at 2 sample/Symbol to 1.5 sample/Symbol

I was looking for some feedback on conversion of equalizer/filter coefficients at different sampler rate. Problem Statement: We have built a transmitter system whose output is at 1.5 sample/symbol (...
199 views

### Unscented Kalman Filter - Multiple Consecutive Measurement Updates

In trying to implement an Unscented Kalman Filter (UKF), I have come across the issue of what to do when my measurement signals come in at a different rate than my control inputs, which I use in the ...
29 views

### What does it mean for a Wavelet transform to commute with translations?

Referencing this article here https://arxiv.org/pdf/1203.1513.pdf It states "A wavelet transform commutes with translations, and is therefore not translation invariant". Now I understand why it is a ...
153 views

### Extracting narrow-band ZigBee signals(4 MHz) from a wide-band WiFi signal(20 MHz)?

I am planning the following. First sample the 20 MHz WiFi channel (WiFi channel-1 in figure). Put band pass filters (5 MHz wide) around each of the ZigBee center frequencies (11, 12, 13, 14). Re-...
386 views

### Simulating the impulse response of a multirate digital filter

I have designed a CIC filter in Verilog and I would like to test its impulse response, but I am not sure where to start from. My input sampling frequency is 51200Hz, the filter is a third order ...
21 views

### Using a Multirate FFT system to analyse audio

I am trying to implement a multirate fft system to try and achieve frequency windowed analysis of audio. Say I have managed to get an impulse response of a system. This impulse may be say one ...
37 views

### DTFT of even and odd samples

Here to find DTFT of $h(2n)$ they have scaled omega, while in RHS to find DTFT $x(2n+1)$ they didn't, why is that?
29 views

### Polyphase components Spectrum formula in Discrete time

I am trying to understand the meaning behind some of the components of the formula for polyphase components in discrete time. Note that $\Omega$ indicates discrete in this notation and the formula is ...
27 views

### Seperation of multi-carrier signal using Square Root Nyquist filter

My goal is to separate multi-carrier to single carrier outputs. I intend to do it using Polyphase FBMC. Each of my carrier is 10 MHz in bandwidth. I have 256 such carrier in the channel. Thus I ...
52 views

### Sampling rate conversion and polyphase decomposition

Can someone please explain the answer to this problem: The sampling rate of a baseband signal shall be converted from 5 kHz to 7.5 kHz using the efficient polyphase implementation with a 'rotating' ...
52 views

### How should I modify my filter coefficients for the filter to be unaltered, when I change my sample rate

I am guessing this is a commonly encountered problem, but I am lost on how to really solve it. I have FIR filter coefficients that are used to match the frequency response of data sampled at 3 kHz. I ...
135 views

### Sampling multiple sensors at different rates

I have a question regarding how best to sample data from multiple sensors when they are all updating at different/changing rates. I am new to data acquisition so please bear with me. For my Master's ...
59 views

### Information Loss in a Multirate System

Assume $M=3$ and $L=2$ for the multirate system shown below. Furthermore, assume an arbitrary fourier transform $X(e^{j\Omega})$. This one lies between $-\pi$ and $\pi$. The fourier transform after ...