Questions tagged [multirate]

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Perfect reconstruction in two-channel filter bank

[from Discrete-time Signal Processing by Oppenheim and Schafer, 3rd ed.] I was not able to prove this: If the analysis and synthesis filters are ideal so that they exactly split the band 0 ≤ |ω| ≤ π ...
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1answer
44 views

Downsampling after a highpass filter

Question: The following sentence is not clear to me (especially why down-shift occurs). Could someone explain it please? On the other hand, downsampling the output of the highpass filter down-shifts ...
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1answer
51 views

Interpolated FIR filter (from Oppenheim and Schafer's Discrete-Time Signal Processing, 3rd ed)

[from Discrete-time Signal Processing by Oppenheim and Schafer, 3rd ed., p.196] Two questions: In this context, the filter with system function represented by Eq. (103) is called an interpolated FIR ...
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1answer
44 views

Group Delay of Mulitrate system

how do I find the group delay of multirate system.(sample rate converter) , IIR non-linear phase filter Say decimation by 2 (with lpf) = tf1(num,den) then again decimation by 2 (with lpf) = tf2(num,...
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1answer
45 views

What are the 'phases' in this 2D scaler filter

I am pretty new to DSP and have been looking at how image scaling is done in hardware. I and came across a 2D scaler core for an FPGA here. I have read up a bit about polyphase filters, but am ...
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1answer
52 views

Where is the mother wavelet defined in the Fast Wavelet Transform?

Referring to the Fast Wavelet Transform, this transform is implemented as a QMF filter bank. This algorithm consists of high/low pass filtering and subsampling. However, a wavelet transform is ...
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61 views

What is the multiplication rate in FIR filter

Consider a system implementing a rational sampling rate change by 5/7: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency pi/7 and a downsampler by 7. The lowpass filter is a ...
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1answer
55 views

Decimation FFT Result

In my Signal Processing class we just learned decimation however after messing around in Matlab trying an example of decimation, I just can't understand what's happening. I get the introducing twi ...
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1answer
68 views

How to figure out number of multiplications in rational sampling

I am trying to understand the following: Consider a system implementing a rational sampling rate change by $\frac{5}{7}$: for this, we cascade upsampler by 5, a lowpass filter with cutoff frequency $\...
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0answers
26 views

Kalman Filter - combining data from sensors with different measurement rates, does one have a good source where i can get more information about it?

someone already wrote a question about the topic, and thats exactly what i am looking for but i need a source to get more information and to cite from in my work i combine 2 kalman-filter for ...
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33 views

When is it possible to swap expander and compressor?

In the figure below I want to know when is it possible to swap expander and compressor so that the outputs remain the same? I know in general it's not possible to interchange because neither expander ...
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1answer
30 views

Save computational burden by calculating the output of decimate filter at output rate?

I read in a book that the output of a decimate filter can be calculated at output sampling rate. In this way the number of filtering operations can be greatly reduced. But I am wondering how to ...
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146 views

Using FFT for implementing a filter bank

I am trying to use Fast Fourier Transform (FFT) for decomposing an audio signal into 8 sub-bands according to this link but the problem is the frequency response of the result contains only the first ...
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1answer
72 views

Decimating Polyphase Filter in Simulink

I have read many of the articles on the website regarding a polyphase decimating filter structure. I'm sure we are all familiar with the typical image shown in Fred Harris Multirate book and many ...
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1answer
258 views

What’s a good book on multi-rate dsp?

Was Studying a dsp design recently with many decimation and interpolation filters, and was wondering if there is a recommended book specifically on the subject of multi-rate dsp? Preferably a book ...
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3answers
82 views

Upsampling with time offsets

Suppose I have done 4x oversampling for a continuous time signal, but the successive sampling times have a linearly increasing offset. Specifically, the samples with indices {4k; k=0, 1, 2,...} are ...
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56 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 ...
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2answers
147 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.
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1answer
105 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?
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1answer
34 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 ...
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0answers
24 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 (...
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1answer
45 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 ...
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1answer
94 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 ...
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77 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' ...
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2answers
124 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 ...
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54 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 ...
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2answers
485 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 ...
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2answers
27 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 ...
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2answers
1k 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 ...
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3answers
418 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 ...
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1answer
95 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 ...
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1answer
323 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 ...
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1answer
117 views

Multirate Signal processing for matching DAC of the SDR

I have been breaking my head for a long time. Please help with this..any input would be helpful! I am trying to implement a OFDM system using SDR (USRPN210 for Transmitter and USRP2 for receiver) ...
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1answer
142 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 ...
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1answer
316 views

Confusion in FFT of Resampled Data

I have the following code in Matlab: ...
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1answer
189 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-...
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1answer
868 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 ...
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1answer
61 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 ...
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1answer
314 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 ...
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1answer
180 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 ...
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0answers
101 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}{\...
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2answers
160 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. ...
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4answers
143 views

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 ...
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2answers
520 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 ...
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1answer
378 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 ...
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3answers
744 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 ...
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2answers
452 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 ...
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2answers
69 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?...