21 votes
Accepted

Python's $\tt resample$ vs $\tt resample\_poly$ vs $\tt decimate$

Downsampling and upsampling are operations that change the sampling rate of a signal. Each one of them is composed of two steps, changing the sampling rate and filtering. Usually, the amount of change ...
  • 10.2k
19 votes
Accepted

Why should an image be blurred using a Gaussian Kernel before downsampling?

An image "should not be blurred using a Gaussian Kernel" in general. This however can be a safe bet for a lot of basic image processing needs, and a smoothing is almost mandatory when you ...
14 votes
Accepted

Which order to perform downsampling and filtering?

You need to filter first and then downsample. Otherwise, you will run into aliasing problems. I.e. frequencies that are above 30 Hz will create images within your frequencies of interest. You can ...
9 votes
Accepted

Downsampling and Gaussian Filtering in the Context of Scale Space Pyramids

You're correct, it has to do with the Cut Off frequency of the Gaussian Blur Filter in its Frequency Domain. In order to see it, just apply a DFT (Using MATLAB it can be achieved by ...
  • 42.6k
9 votes
Accepted

Shannon interpolation formula for downsampled data with an "almost ideal" low pass filter

I don't get your downsample step when you downsampled by factor $M$. Let me go from scratch with the spectrum visualization below, with time domain, continuous frequency domain and discrete frequency ...
  • 5,835
9 votes

Why should an image be blurred using a Gaussian Kernel before downsampling?

According to (digital) sampling theorem, signals should be properly bandlimited, before they are (down) sampled. A practical digital filter approximately limits the bandwidth of the signal and makes ...
  • 27.1k
9 votes

Downsample a signal by a non-integer factor

You need a resampler. There's different resamplers! I'm not sure you're correctly interpreting the answer you cite: you don't just decimate by 647; you'd first (at least mathematically) upsample by ...
8 votes
Accepted

Is this signal perfect reconstructable?

Yes the signal is perfectly reconstructed. Consider the process at each stage as I show using the block diagram below: Consider each sample of the signal at each node in the diagram (each sample is ...
  • 38.4k
7 votes
Accepted

What is the most precise frequency analysis spectrography algorythm?

You don't have a loss in time precision when using FFTs because the FFT is fast. The FFT is just a fast algorithm for implementing the discrete Fourier transform (DFT), nothing more. Instead, there is ...
  • 23.9k
7 votes
Accepted

The Proper Way to Do Sinc Downsampling (DFT Downsampling) for Uniformly Sampled Discrete Signals with Finite Number of Samples

Interpolation in Frequency (DFT Domain) The implementation is well known. In MATLAB it will be something like: ...
  • 42.6k
6 votes

Decreasing Sample Rate in DFT (FFT) for Audio Analysis

There are 2 different things here that we are mixing: Bin Width As you mentioned, the bin width is a function of the ratio between the sampling rate and the number of samples. If you increase the ...
  • 42.6k
5 votes
Accepted

rtlsdr sample rates and nyquist rate

The RTL-SDR, as most software-defined radios, has an analog front-end that includes a tunable mixer. This mixer can down-convert the frequency band you're interested in to baseband, where it is ...
  • 13.9k
5 votes
Accepted

Frequency Representation of Downsampled Signal

In the final result, you want to express the spectrum $X_d(e^{j\omega})$ in terms of $X(e^{j\omega})$, the spectrum of $x[n]=x_c(nT)$. Since $X(e^{j\omega})$ is already periodic, it must be possible ...
  • 81k
5 votes
Accepted

How Is the Bandwidth of an Image Reduced by an Octave in Gaussian Pyramid Procedure?

The model is simple. Assume we have data I0 on the frequencies range of $\left[ 0, 1000 \right] $ [Hz]. We have 2 Black Boxes: ...
  • 42.6k
5 votes

What is the effect of the natural logarithm in the frequency domain?

First note that when you use a logarithmic function you shall avoid negative arguments if it's output should be real valued. Then consider the following relation: $$ y[n] = \ln( 1 + x[n] )$$ where ...
  • 27.1k
5 votes
Accepted

Scipy resample, "fourier method" explanation

Suppose you have initially a real-valued sequence x of length N. The function is basically doing this: To upsample, it ...
  • 4,890
5 votes
Accepted

Decimation vs Mean in downsampling operation

What you are calling decimation is in fact downsampling: keeping one of every $k$ samples from the original signal. Proper decimation involves a digital low-pass filter in order to eliminate all ...
  • 4,761
5 votes

Downsample: resample vs antialias fitlering + decimation

I will explain why method 2 is often a better choice over method 3. The frequency domain approach is equivalent to the "Windowing" method of filter design- in that to do that approach ...
  • 38.4k
5 votes
Accepted

Downsampling and low pass filtering in one step?

Is it possible to combine decimation and low pass filtering in one step? Not necessarily only for images but also for general signals. Yes, that's what people usually do when they implement ...
5 votes
Accepted

Is spectral density conserved after aliasing?

No. The aliased component will interfere with the non-aliased components and the interference can constructive or destructive. Trivial example: $$x[n] = \sin\left(\frac\pi2n\right)$$ If you down ...
  • 34.1k
5 votes
Accepted

Polyphase Decimation Filter parallel inputs

Problem Statement and Bottom Line of Solution As described, the OP wishes to channelize the input bandwidth that extends from DC to fs/2 (f = 0 to +1.25 GHz) into four channels each having one quarter ...
  • 38.4k
4 votes

Downsampling, Filtering and Averaging

Averaging is filtering with a rectangular filter kernel, which has a poor frequency response, both in pass band ripple and stop band attenuation, Because of the poor stop band response it won't anti-...
  • 34.1k
4 votes
Accepted

Difference between Sub Sampling and Down Scaling of Images

When we have a discrete signal it is usually sampled on a grid of indices. Both sub sampling and down scaling changes the grid. The classic definition is that Sub Sampling is a step in Down Scaling. ...
  • 42.6k
4 votes

Upsample / Downsample a Signal from 1920.93Hz to 1920Hz

You can attack this in 2 approaches: Interpolation. Resample. Interpolation Build a new time grid as you wish and use Kernel to interpolate data. Since you need to make a small change even a Linear ...
  • 42.6k
4 votes
Accepted

Cut-off frequencies for fractional sample rate adjustment

Don't be confused; you're doing everything correctly here: $$\begin{align*} f_{sample,in} &&\overset{\text{interpolate}}{\rightarrow}&& f_{sample,intermediate} &&\overset{\...
4 votes
Accepted

Downsampling and Then Upsampling

You will get $Y(z) = \frac1M\sum_{m=0}^{M-1} X(e^\frac{-j2\pi{m}}M*z)$ If you were to upsample first and then downsample you would get $Y(z) = \frac1M\sum_{m=0}^{M-1} X(e^{-j2\pi{m}}*z)$ which ...
  • 156
4 votes

Random sampling vs uniform sampling

The key idea is that the random sampling approach enforces more constraints on the resulting signal than the uniform sampling approach does. The POCS (projections onto convex sets) algorithm used for ...
  • 23.1k
4 votes
Accepted

The relationship between downsampling and frequency resolution

Your understanding is correct. I don't have the full text of the paper, but it sounds like they aren't being very precise with their description. As you pointed out, downsampling doesn't improve ...
  • 23.9k
4 votes

Aliasing after downsampling

See this good mathematical treatment of undersampling by Prof. Fowler at Binghamton University, using the comb function as you have done in the time domain, taking the z-transform of the resulting ...
  • 38.4k
4 votes

Which order to perform downsampling and filtering?

Since I can't comment on this particular site I'd say this, consider the following before you do what you're trying to do. Due to the Nyquist law you want your sampling frequency to be that of the ...
  • 141

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