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Questions tagged [sinc]

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What are the advantages of using the Dirichlet kernel for interpolation?

Suppose we define the Dirichlet kernel as: $$ \frac{\sin(\pi N x /2)}{\pi N\sin(x /2)} $$ (Note: I'm not entirely sure what the standard definition of the Dirichlet kernel is; mine is slightly ...
Gillespie's user avatar
  • 1,797
1 vote
1 answer
87 views

Signal recovery is based on the development of the Shannon sampling theorem?

One of the earliest extensions of this theorem was stated by Shannon himself in his 1949 paper, which says that if $x(t)$ and its first $(M - 1)$ derivatives are available, then uniformly spaced ...
Son VuHoang's user avatar
2 votes
1 answer
54 views

Digital Audio Resampling

I've been working from this reference document, essentially trying to recreate Figure 7 with the understanding that the two functions place_signal and ...
Michael Blazej's user avatar
0 votes
1 answer
41 views

Since harmonics only generate at multiples of the center freq, is it for this reason that the left part of a FT (like sinc) has no physical meaning?

If we have a rectangular pulse function, we know that after a Fourier transform we obtain a sinc: We know that the left part (negative frequencies) has no physical meaning and it's just specular. It'...
allexj's user avatar
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13 votes
4 answers
3k views

Why is the time domain low-pass filter the "sinc" shape?

Consider: I'm looking at low-pass filters, and I see that the time domain representation of an "ideal" filter resembles the shape above whereas the frequency domain is a box. I also get the ...
thepman's user avatar
  • 133
0 votes
1 answer
113 views

Filtering in time domain vs filtering in frequency domain

The signal is an impulse repsonse. I am filtering the signal using a windowed sinc filter in both frequency and time domain. I am interested in knowing the differences between the two methods and ...
Tanmayee Pathre's user avatar
1 vote
0 answers
118 views

How can the DCT be used for bandlimited interpolation?

I know the discrete cosine transform (DCT) is used for compression, but can anyone give an example of how to use it for bandlimited interpolation? One way might be zero-padding in the DCT domain and ...
Gillespie's user avatar
  • 1,797
3 votes
1 answer
415 views

java resampling implementation using sinc function

To be as succinct as possible, I've written a Java method that implements resampling of a signal using the sinc function interpolation formula. When I test this code with a simple sinusoid, I'm able ...
Richard Sand's user avatar
0 votes
1 answer
85 views

Intuition for how much ringing a particular filter will induce

I've seen figures in various books about the the tradeoff between aliasing and blurring when using a gaussian-like filter: the narrower it is, the more it cuts off low frequencies and thus blurs it, ...
multiscale's user avatar
4 votes
1 answer
434 views

Fourier Transform of impulse train proof in Julius O Smith's textbook

$\DeclareMathOperator{\sinc}{sinc}\DeclareMathOperator{\asinc}{asinc}$I'm trying to follow the proof of the Fourier Transform for an Impulse train given in Julius Smith's textbook. I come across the ...
Tim Mak's user avatar
  • 225
0 votes
2 answers
670 views

Designing a digital band pass filter with Sinc filter in time domain

I want to design a sinc filter in the time domain (a bandpass filter in the frequency domain). I wrote test code in python to investigate, and would appreciate help understanding it and answer my ...
Captain's user avatar
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2 votes
0 answers
64 views

Synthesizing a pure tone in Frequency Domain: can it be done more efficiently?

I came to the conclusion that synthesizing pure tones in Frequency Domain is much less efficient than synthesizing cosines in Time Domain and then computing the FFT. But I suspect this is the case ...
elena's user avatar
  • 351
2 votes
1 answer
364 views

Applying Kaiser Window to sinc interpolation

I am trying to apply the kaiser window during sinc interpolation. The following is my sinc interpolation code: ...
Hari's user avatar
  • 93
5 votes
2 answers
923 views

Odd artifacts after sinc interpolation

I am trying to upsample a signal using sinc interpolation. I have written a way to do this in python. ...
guitardenver's user avatar
3 votes
2 answers
847 views

Why use sinc function to downsample an image in fourier domain?

I'm very confused about downsampling in image processing and the use of sinc function to do it. I read this post [1]: 2D Fourier downsampling some time ago that talked about my own doubt, that is to ...
overflow''s user avatar
0 votes
3 answers
493 views

Convolution of squares / boxcars in functional form

$$ \Pi(t/A) * \Pi(t/B) $$ where $$ \Pi(t) = \begin{cases} 1,\ -1/2 \leq t \leq 1/2 \\ 0,\ \text{otherwise} \end{cases} $$ How to compute? Derivation/steps optional but welcome. Note: I'm aware of ...
OverLordGoldDragon's user avatar
1 vote
1 answer
135 views

Convolve sinc trains

$$ \begin{align} & \mathrm{sinc}(As + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/A)\ \star \\ & \mathrm{sinc}(Bs + .5)\sum_{n=-\infty}^{\infty} \delta (s - n/B) \end{align} $$ How to compute? ...
OverLordGoldDragon's user avatar
2 votes
1 answer
587 views

Fractional Frequency Shifting a Discrete Signal in the Frequency Domain

In our current hardware-based signal processing pipeline, we have a time-domain signal $x[n]$ that we want to frequency shift by $f_0$. To do this, we multiply the signal by a complex exponential in ...
Logan's user avatar
  • 55
3 votes
1 answer
2k views

Impulse response of IIR low-pass filter

(Disclaimer. I have started doing some DSP. The last time I worked with this was in the eigthies. And I wasn't much of a specialist then, either.) Is the impulse response different for IIR and FIR ...
Øyvind Teig's user avatar
2 votes
1 answer
76 views

Is the ideal reconstruction process BIBO stable?

It is well known that ideal lowpass filter, i.e. the lowpass filter whose impulse response is $h(t) = \text{sinc}(t)$, is not BIBO-stable because $h(t)$ is not absolutely integrable. However, think ...
avril_14th's user avatar
3 votes
1 answer
486 views

Downsampling an image using sinc interpolation?

I have a discrete image of size $2^N \times 2^N$ which I would like to iteratively downsample to produce a pyramid with image sizes $2^k\times 2^k, \, k=0,\ldots,N$. That is, each subsequent image ...
lightxbulb's user avatar
1 vote
1 answer
201 views

How do I confirm that range cell migration correction was done correctly? Is there a way to check this graphically without looking at the signal data?

I am implementing the Range Doppler Algorithm for a Synthetic Aperture Radar project and I am at the step where I must perform Range Cell Migration Correction. This step involves creating a sinc ...
level2fast's user avatar
2 votes
2 answers
611 views

Differences in transforming a sinc FIR filter from lowpass to highpass using spectral inversion and spectral reversal

I have designed a lowpass sinc 1023 tap FIR filter with a Blackman window and this works fine. I understand there are then two ways to transform this lowpass filter to a highpass one. One is spectral ...
MikeDB's user avatar
  • 123
1 vote
0 answers
316 views

Triangular dither - What does it mean to say that an input signal is uncorrelated with the dither

In the oft-cited ADC dithering appnote: Oversampling Techniques using the TMS320C24x Family http://www.ti.com/lit/pdf/spra461, it notes under triangular dither: However, this approach requires that ...
Shrikumar's user avatar
0 votes
2 answers
631 views

Inconsistency Between Analysis and Simulation Results of Fourier Transform of a Sinc Function

First of all, hello. This question is about a problem that I’ve faced during an attempt to obtain both time and frequency responses of a sinc function in MATLAB. The problem is an inconsistency ...
Karakoncolos's user avatar
0 votes
1 answer
110 views

Output of a linear time-invariant(LTI) system

I am very confused about one of the questions I received during an exam. How do I solve this question?
Alan Chen's user avatar
1 vote
2 answers
405 views

How do I sort out my window sinc low pass filter

I started writing a windowed sinc low pass filter, but I cannot seam to get the code figured out right. I followed these two links http://doctord.webhop.net/Courses/textbooks/Smith_DSP/dsp_book_Ch16....
Edward Eddy67716's user avatar
1 vote
0 answers
992 views

Sinc3 Filter in FPGA

I working on FPGA block which requires an Sinc3 Filter for Sigma-Delta ADC coming in. I read about it and Sinc filter, is filter with frequency response of sinc, that means its just a moving average ...
Michael Rahav's user avatar
1 vote
1 answer
4k views

How to correctly use sinc interpolation in Matlab?

What is the right way to use sinc interpolation for a given discrete signal $x[n]$? Following is the sinc interpolation formula: $$x(t) = \sum_{n=-\infty}^\infty x[n] \mathrm{sinc}\left(\frac{t-nT}{T}\...
level2fast's user avatar
0 votes
0 answers
93 views

Fourier transform and energy of a convolution

Hi guys i have to find the fourier transform of the convolution: $$ sinc(t/2T)*\sum\limits_{n-\infty}^{+\infty} (-1)^{n}\delta(t - nT) $$ i was thinking of express the summatory as : $$\sum\limits_{n-\...
Giovanni Cerciello's user avatar
0 votes
1 answer
95 views

how sinc pulses can be used to distinguish different symbols

Let's say we want to transmit a sequence of numbers Using PAM, this sequence is transmitted with the signal $s(t)$ The pulses in $s(t)$ are transmitted at a rate $R_p=\frac{1}{T_p}$. This is called ...
Noha's user avatar
  • 349
0 votes
0 answers
222 views

Rectangular Pulse Train and Sinc Function

I wanted to ask that in frequency domain the rectangular pulse is a sinc function, so is this sinc function periodic or aperiodic? Also if signals that are continuous in time domain then they are ...
Ahmad Qayyum's user avatar
1 vote
0 answers
300 views

Convolution of Heaviside function with a sinc low pass, is it band limited?

Is the result of convolution of a heaviside function with a sinc low pass with cut off at fc, say 25khz, band limited ((sin(2 x Pi x fc x i))/(Pi x i))? I've been working it out in frequency domain (...
Manuel Jenkin's user avatar
0 votes
0 answers
83 views

Sinc Low pass and transients

Assume, I am trying to use a 50khz sampling rate for some signal. I don't know what the spectrum of input signal is, so I will have to low pass manually with sinc (theoretical best low pass) to band ...
Manuel Jenkin's user avatar
2 votes
1 answer
329 views

How to prove a train of sinc pulses in digital communicaton system are orthogonal to each other?

Consider a train of sinc pulses: $$\phi_n(t)= \frac{\sin(\omega_M(t-nT_s))}{\omega_M(t-nT_s)}\quad; n=0,\pm1,\pm2,\dots$$ $\quad$where,$\quad T_s=\frac{\pi}{\omega_M}$ Now ,in order to show sinc ...
Suresh's user avatar
  • 285
2 votes
1 answer
2k views

How to implement sinc interpolation

I'm trying to write my own high quality audio sample rate converter. I barely know anything about signal processing though so I need help. From what I understand I need to sum together normalized sinc ...
sincman's user avatar
  • 23
3 votes
1 answer
3k views

Getting the power of a signal from its Fourier transform?

I have a non-periodic signal that contains the sinc function in the time domain and so it is a bit difficult to calculate its power (because of the integral) through: $$ {P_x} = \lim_{T \to \infty} \...
Bram Fran's user avatar
1 vote
1 answer
201 views

DTFT and a Downsampled Sinc Function

I found the answers to this question and this question to be extremely helpful in understanding the derivation of the downsampling or decimation property of the DTFT. Thank you! I am now struggling ...
Steve J.'s user avatar
2 votes
3 answers
736 views

aliasing in image processing

I know that aliasing occurs when a signal is subsampled. If the sampling rate is lower than twice the max frequency in a signal, aliasing occurs. How is it in pictures? as far as I know, a sinc-filter ...
Khan's user avatar
  • 141
1 vote
2 answers
1k views

Why notches in sinc filter response

Below response shows sinc1,sinc2 and sinc3 filter response. I understand that notches in the frequency response happens at the output data rate of the sigma-delta ADC. But I am not able to figure out ...
Naveen Sajjanar's user avatar
1 vote
1 answer
77 views

How $\Delta f=\frac{1}{2T}$ satifies the orthogonality condition?

Let $$s_{ml}(t)=\sqrt{\frac{2E}{T}}\exp(j2\pi\Delta fmt)$$ where $T$ is the time-period of signal $\Delta f$ is the frequency spacing The text says that two signals $s_{ml}(t)$ and $s_{nl}(t)$ are ...
Userhanu's user avatar
  • 181
1 vote
1 answer
755 views

Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$

Find the Discrete-time Fourier transform of $\frac{\cos(\frac{n\pi} 6)}{(n+3)\pi}$ I thought of making it to be a sinc, but at the bottom there is $n+3$ and if I replace $n+3$ then I don’t know how ...
Vitali Pom's user avatar
0 votes
1 answer
183 views

Sinc Interpolation Artifacts

I have written a program that uses sinc interpolation to resample some data. The general algorithm is a that I compute the previous N values and the next N values to get a new sample at a non-integer ...
Matt Eddy's user avatar
0 votes
4 answers
85 views

How do I prove that delta - sinc function is the same as an (-1)^n times the sinc

$$\delta(n) - \frac{1}{2} \mbox{sinc} \left(\frac{n}{2}\right) = (-1)^n \frac{1}{2} \mbox{sinc} \left( \frac{n}{2} \right)$$ The picture shows what I've tried
M.Bore 's user avatar
0 votes
2 answers
127 views

ZOH non ideal sampling loss formula

Hello i am trying to calculate the amplitude loss of non ideal sampling. My signals amplitude is 10 at 70 frequency. When we sample it at Fs=400 we have al 0.511 loss as shown in plot bellow. How can ...
rocko445's user avatar
  • 171
0 votes
1 answer
452 views

Reconstruction using sinc

The signal that I produce above. What is the reason for it to slide to the right? In oversampling at Nyquist rate can I make like below picture ? do you think the signal i produced at nyquist rate is ...
Oğuzhan Kırlar's user avatar
1 vote
1 answer
1k views

Convolution Integral of Harmonic Signal (Cosine) with the Sinc Function

I was asked to show that this convolution integral results in the answers also given in the image. Not quite sure how to approach this integral, everything seems to be coupled together. Does anyone ...
Alalalala's user avatar
-1 votes
1 answer
34 views

Impulse coefficient when it does not match the bin index

Assume that I have a N=10 samples with Fs=10. assume in the time domain an unit impulse event happens which should be placed at 3.425 index in time domain. Assume that I could not change Fs or ...
learner8059's user avatar
2 votes
1 answer
2k views

windowed sinc filter in matlab

Hello i'm designing a low pass filter windowed sinc in matlab ...
carterwild's user avatar
0 votes
1 answer
71 views

Purely theoretical question about idelal filters and infinite oscillations

I am asking perhaps a naive question, but still, it would be nice to have this formally stated one time: in theory, if we could do it (of course, we cannot, but imagine we could), if we could ...
SheppLogan's user avatar