Questions tagged [scaling]
40 questions
10
votes
3 answers
why should I scale the fft using 1/N?
I am writing a report, and my advisor asked me to explain why I scale the fft by a factor 1/N (where N is the length of the array).
I used to use the scaling convention of multipling the fft by the time increment (dt), this convention was good for…
Luca Mirtanini
- 404
- 3
- 12
5
votes
1 answer
Algorithm that enlarges the image to a resolution of $2N \times 2N$ using DFT operations
I'm trying to solve the following question:
Given an image at a resolution of $N \times N$. Describe an algorithm that enlarges the image to a resolution of $2N \times 2N$ using DFT operations.
As I understand, we need to use the DFT, split it…
vesii
- 173
- 4
4
votes
3 answers
Pixel Binning: Effect on SNR for Hardware vs. Software Binning
Is there a difference in SNR (or any other measure of image quality) between using 2x2 pixel binning in the camera and shrinking the full resolution image in software (cv::INTER_AREA) to the same size (w/2, h/2) ?
I imagine that SNR is higher with…
ezekiel
- 163
- 2
4
votes
2 answers
Factor $|a|^{-1/2}$ in definition of mother wavelets
The mother wavelet is defined as
$$\Psi_{a,\tau}(t) = \lvert a\rvert^{-1/2}\Psi\left(\frac{t-\tau}{a}\right)\tag{1}$$
in which the factor
$$ \lvert a\rvert^{-1/2}\tag{2}$$
is supposed to serve that
$$\lVert\Psi_{a,\tau}\rVert =…
Starhowl
- 371
- 2
- 15
3
votes
2 answers
Impulse response of a time scaling system
Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system?
\begin{array}{l}
X( \omega ) \ =\ \int ^{\infty }_{-\infty } x( t) e ^{-j\omega t} dt \\
Y( \omega ) \…
user8206055
- 31
- 3
3
votes
1 answer
How to "scale" the FFT when using it to calculate discrete convolution?
As you probably know, the discrete convolution $ H = F \ast G $ of some $ F \left[ x \right] $ and some $ G \left[ x \right] $ can be calculated using the Fast Fourier Transform (FFT).
To do this, one would ...
Set $ M $ to the length of the…
andrep
- 33
- 6
2
votes
1 answer
How to improve accuracy while converting floating point coefficients to fixed point in the case of an all pole IIR filter
I am having an all pole IIR filter of order 5 with floating point filter coefficients
[1,
-4.708642687,
9.963818327 ,
-11.99038368,
8.647611478,
-3.553230696,
0.659454607].
When an impulse input was applied to the IIR filter, the first…
Deepa
- 39
- 6
2
votes
3 answers
Time scaling and shifting of delta function
Learning signals and systems.
Solving time scaling and shifting problems.
For the question
$$x(t) = u(2t - 1)$$
First we shift by 1 to the right side and then we do time scaling , i.e divide by 2 on the time axis.
$x(t) = δ(2t - 1) $
Can we do the…
Tejas
- 25
- 1
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2
votes
3 answers
Theoretical Maximum of DFT
For any discrete input signal between +1 and -1, what is the theoretical maximum DFT?
If the input is a cosine of $N$ samples with amplitude $A$, the peak spectral magnitude is $A*N/2$. But what about any arbitrary waveform?
A square wave with the…
Karl Haebler
- 99
- 6
2
votes
1 answer
Implementation of IIR Filter in dsPIC 33EP - Scaling
I have to implement an IIR controller in dsPIC 33EP (16-bit, fixed-point, two's complement, wrap-around, 40-bit accumulator, 32-bit multiply, 12-bit ADC) and I am using cascaded, Direct Form I second order sections (ordering up).
Now, I am having…
Ben
- 33
- 2
1
vote
1 answer
Fourier transform of time-scaled signum function
I have the signals $x_1(t)=\mathrm{sgn}(9t)$ and $x_2(t)=\mathrm{sgn}(t/5)$, where $\mathrm{sgn}$ denotes the signum function: $-1$ or $+1$ depending on the sign of the argument. I computed their Fourier transforms as $$X_1(f)=\frac{1}{j\pi(f/9)}$$…
fjordi
- 23
- 4
1
vote
1 answer
Building the low pass filter in the wavelet scattering transform
In 1, analyzing the equivalence between MFCC and wavelet transform, the scaled wavelets are truncated for $\lambda < 2\pi Q/T$ to fit the time spread of the wavelets within the length $T$ of the window. The lower part of the spectrum is divided into…
dac
- 77
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1
vote
0 answers
Calculate ScaleVlues of IIR Filter manually from sosMatrix of MATLAB
while using "design" in matlab to design filters, at the output we can see a ScaleValues matrix that is used to compensate for overflow problem. my question is that how this matrix is calculated? I want to manually calculate it using sosMatrix and…
Saeed Hatami
- 11
- 1
1
vote
3 answers
Whether $y(t) = x(t/3)$ is a memoryless system?
I am a newbie in signal and system, and feeling confused about the memoryless property, it says at the definition, if a system gives output only depends on present input, then its memoryless. So if at $t=3$, $x(1)$ is needed, whether this count as a…
Tie
- 11
- 1
1
vote
1 answer
Correctly scaling FFT of different lengths
I have been looking at using two FFTs of different lengths and displaying the output magnitudes on the same graph (a shorter length window for the higher frequencies, and a longer one for lower frequencies).
Currently, I find my impulse response by…
samp17
- 153
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