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Sampling and Reconstruction of digital signal in Matlab. Oguzhan Kirlar about 1 hour ago. Vote 0. Edited: Oguzhan Kirlar about 1 hour ago. Screenshot from I'm trying to write a program in Matlab that samples using Nyquist theorem and recovers signal.

However, I cannot write sampling part for sum of 2 signal. I write this code.

**Sampling Signals Part 3 (3/4) - Image Downsampling and Reconstruction in Matlab**

I want to draw Undersampling, sampling at Nyquist rate and oversampling. When make researching, I find code like that, but i cannot use it for my signal. What is fm in my signal? How can i find it?

I want to write a code like above for all 3 cases. And how can I find the Nyquist sampling rate for signal empirically?By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information.

When I type in the following code, I'm instead getting something very noisy--not what I am looking for. What am I doing wrong? Thank you in advance! You are not accumulating the reconstructed samples properly.

Specifically, you are only retaining one value from the resampled signal, not all samples. This means that you don't have to multiply the argument by pi. Recall that the reconstruction formula requires the normalized sinc function, so there is no multiplication of pi in the argument of the function.

To make things more efficient, definitely use the sum function but do it over all samples.

## Sampling and Reconstruction of digital signal in Matlab

So your for loop should now be:. You can accomplish the same thing, but more efficiently, using the discrete Fourier transform DFT :. What is happening here is that I'm padding the DFT as computed efficiently using fft with zeros to the desired size. The inverse transform then results in the signal interpolated using the sinc interpolator. To preserve the signal strength some normalization is needed. Any differences you see with Rayryeng's answer is due to the periodic nature of the DFT: basically the sinc functions, as they exit the signal domain on the right, come back in at the left; the data at the right end of the plot influence the result at the left end of the plot and vice versa.

To learn more about interpolation using the Fourier transform, see this blog post. Learn more. Asked 2 years, 2 months ago. Active 2 years, 2 months ago.

Viewed 2k times. Christiana S. Chamon Christiana S. Chamon 10 10 bronze badges. So did any of our answers help? So sorry I forgot to comment back. Chamon Feb 9 '18 at No worries. When you're ready, go ahead and accept any one of our answers to let the community know you no longer need help.Documentation Help Center. This example shows how to reconstruct missing data via interpolation, anti-aliasing filtering, and autoregressive modeling. With the advent of cheap data acquisition hardware, you often have access to signals that are rapidly sampled at regular intervals.

This allows you to gain a fine approximation to the underlying signal. But what happens when the data you are measuring are coarsely sampled or otherwise missing significant portions? How do you infer the values of the signals at points in between the samples that you know?

Linear interpolation is by far the most common method of inferring values between sampled points. You need to sample a signal at very fine detail in order to approximate the true signal. In this example, a sinusoid is sampled with both fine and coarse resolution. When plotted on a graph, the finely sampled sinusoid very closely resembles what the true continuous sinusoid would look like. Thus, you can use it as a model of the "true signal.

It is straightforward to recover intermediate samples in the same way that plot performs interpolation. This can be accomplished with the linear method of the interp1 function. The problem with linear interpolation is that the result is not very smooth. Other interpolation methods can produce smoother approximations. Many physical signals are like sinusoids in that they are continuous and have continuous derivatives.

You can reconstruct such signals by using cubic spline interpolation, which ensures that the first and second derivatives of the interpolated signal are continuous at every data point:. Cubic splines are particularly effective when interpolating signals that consist of sinusoids.

However, there are other techniques that can be used to gain greater fidelity to physical signals which have continuous derivatives up to a very high order. The resample function in the Signal Processing Toolbox provides another technique to fill in missing data. Like the other methods, resample has some difficulty reconstructing the endpoints.

On the other hand, the central portion of the reconstructed signal agrees very well with the true signal. The technique works best when the signal is sampled at a high rate. In the following example, we create a slowly moving sinusoid, remove a sample, and zoom into the vicinity of the missing sample.

The reconstructed sinusoid tracks the shape of the true signal reasonably well, with only a slight error in the vicinity of the missing sample. However, resample does not work well when there is a large gap in the signal.

For example, consider a dampened sinusoid whose middle portion is missing:. Here resample ensures that the reconstructed signal is continuous and has continuous derivatives in the vicinity of the missing points.

However, it cannot adequately reconstruct the missing portion.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing.

It only takes a minute to sign up. I have a wav file recorded from my smartphone's mic, and I want to reconstruct the sampled signal and plot the reconstructed signal. After some research and search, I was able to get the following code:. But it looks like I can't get my desired output, I'm completely new to signal processing, can someone tell me what is wrong with my code?

Thank you! Update 1: I just realized that I used a fairly high sample rate hzso I tried downsampling using the following code:. Update 3: I just found the following code that seems do the same thing, is this right? If so I don't need to implement it myself. The term reconstruct has a special meaning in DSP and is related to converting a signal from discrete form to continuous using a DAC and a low-pass filter.

I'm going to guess that you are just looking to plot the signal in time domain, and if that is the case then your code would look like this:. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Sampled signal reconstruction using matlab Ask Question. Asked 6 years, 11 months ago. Active 6 years, 3 months ago. Viewed 9k times.

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## Reconstructing Missing Data

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You may receive emails, depending on your notification preferences. Sampling and Reconstruction of digital signal in Matlab. Oguzhan Kirlar circa un'ora ago.Documentation Help Center. This example shows how to reconstruct missing data via interpolation, anti-aliasing filtering, and autoregressive modeling.

With the advent of cheap data acquisition hardware, you often have access to signals that are rapidly sampled at regular intervals. This allows you to gain a fine approximation to the underlying signal. But what happens when the data you are measuring are coarsely sampled or otherwise missing significant portions?

How do you infer the values of the signals at points in between the samples that you know? Linear interpolation is by far the most common method of inferring values between sampled points. You need to sample a signal at very fine detail in order to approximate the true signal.

In this example, a sinusoid is sampled with both fine and coarse resolution. When plotted on a graph, the finely sampled sinusoid very closely resembles what the true continuous sinusoid would look like. Thus, you can use it as a model of the "true signal. It is straightforward to recover intermediate samples in the same way that plot performs interpolation.

This can be accomplished with the linear method of the interp1 function. The problem with linear interpolation is that the result is not very smooth. Other interpolation methods can produce smoother approximations. Many physical signals are like sinusoids in that they are continuous and have continuous derivatives. You can reconstruct such signals by using cubic spline interpolation, which ensures that the first and second derivatives of the interpolated signal are continuous at every data point:.

Cubic splines are particularly effective when interpolating signals that consist of sinusoids. However, there are other techniques that can be used to gain greater fidelity to physical signals which have continuous derivatives up to a very high order.

The resample function in the Signal Processing Toolbox provides another technique to fill in missing data. Like the other methods, resample has some difficulty reconstructing the endpoints.

On the other hand, the central portion of the reconstructed signal agrees very well with the true signal. The technique works best when the signal is sampled at a high rate.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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### Sinc Interpolation for Signal Reconstruction

It only takes a minute to sign up. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Shannon interpolation formula for signal reconstruction on Matlab Ask Question. Asked 3 years, 2 months ago. Active 3 years, 2 months ago. Viewed times. Now I tried to plot this on Matlab, but with no success. Jason Born Jason Born 1, 7 7 silver badges 16 16 bronze badges. Try what I said : start from a discrete signal, downsample and recover it from the interpolation theorem.

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