Questions tagged [discrete-signals]

A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities.

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16
votes
2answers
14k views

What are advantages of having higher sampling rate of a signal?

Being a non signal processing science student I have limited understanding of the concepts. I have a continuous periodic bearing faulty signal (with time amplitudes) which are sampled at $12\textrm{ ...
31
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6answers
136k views

Difference between discrete time fourier transform and discrete fourier transform

I have read many articles about DTFT and DFT but am not able to discern the difference between the two except for a few visible things like DTFT goes till infinity while DFT is only till N-1. Can ...
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2answers
249 views

DFT exercise in the book Understanding digital signal processing 3 Ed

I am trying to solve exercises from the book Understanding digital signal processing 3 Ed - Richard Lyons. I will repeat the question as it is in the book: 3.3 We want to calculate an N-point DFT ...
0
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3answers
2k views

How to implement Polyphase filter?

I am trying to implement the following 4-Tap Polyphase window shown in figure below and used in : polyphase filters- radio astronomy: lecture #8 by Prof. Dale E. Gary on Matlab. I have tried splitting ...
12
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9answers
837 views

Where is the flaw in this derivation of the DTFT of the unit step sequence $u[n]$?

This question is related to this other question of mine where I ask for derivations of the discrete-time Fourier transform (DTFT) of the unit step sequence $u[n]$. During my search for derivations I ...
6
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1answer
2k views

Zero Padding of FFT

There are many question related to the zero padding a time domain signal to get more frequency bins after performing Fourier transform. As I understand this process is equivalent to trigonometric ...
5
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1answer
4k views

Analytically designing a notch-filter for specified frequency 50 Hz

I tried to analytically construct a causal notch filter that stops frequencies at 50Hz and I thought if zeros are more than poles it will be non-causal so I chose equal amount of poles and zeros ...
18
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1answer
25k views

Help calculating / understanding the MFCCs: Mel-Frequency Cepstrum Coefficients

I've been reading bits and pieces online but I just can't piece it all together. I have some background knowledge of signals / DSP stuff which should be enough prerequisites for this. I'm interested ...
9
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3answers
9k views

What is the difference between natural response and zero input response?

I am new to DSP and was going through different responses of a system subjected to an input. My understanding of zero input response is: it is the response/output of the system when the input signal ...
4
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2answers
4k views

How to remove or filter the drift problem in measured Strain signal?

I have the strain signal of a lateral beam of a car measured at sampling rate 1,200Hz from data acquiring system. Even after using temperature compensation in strain gage, we are getting drift. So I ...
26
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4answers
15k views

How to Extrapolate a 1D Signal?

I have a signal of some length, say 1000 samples. I would like to extend this signal to 5000 samples, sampled at the same rate as the original (i.e., I want to predict what the signal would be if I ...
17
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8answers
6k views

Is there an algorithm to compute the phase for a single frequecy?

If you have a function $f(t)=A \cdot \sin(\omega t+\phi)$, and reference sin wave $\sin(\omega x)$ what would be a fast algorithm to compute $\phi$? I was looking at Goertzel algorithm, but it doesn'...
5
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1answer
5k views

Initial conditions for the LTI systems described as a difference equations

Why do we need the initial conditions to be zero for the LTI systems described as a difference equations? First question is why do we need it for linearity? I can't think of any example of the non ...
7
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3answers
4k views

can't find out the period of my signal

I've a noisy signal, which is the sound of motor with a constant speed, so the sound "should" be periodic, I know that there is a way to use the autocorrelation function to get the period,I did it, ...
6
votes
1answer
4k views

1D Deconvolution with Gaussian Kernel (MATLAB)

Suppose that I know the output and the transfer functions of a system and I would like to calculate the input function using deconvolution. To get a grasp of the idea I have created a simple ...
1
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2answers
189 views

FFT Phase interpretation of input signal with non-integer number of cycles in FFT window

It is known that if we take the FFT of a signal at such a frequency which has non-integer number of cycles in the sample window we get different value of phase even if the original signal was at phase ...
1
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1answer
7k views

Properties of Discrete-time Sinusoidal Signal

I was reading in a book that below stated are the Properties of Discrete-time Sinusoidal Signal: Property 1. The discrete time sinusoids whose frequency are separated by an integer multiple of 2$\pi$...
0
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2answers
1k views

Higher order harmonics during sampling

I am studying about the sampling theorem in conjunction for ADC. I got little confused while reading about aliased frequencies. I see that as per the Nyquist theorem, the sampling frequency (fs) ...
4
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1answer
5k views

Understanding the Windowing Method in PSD Calculation

I have some issues understanding the use of a window (it doesn't matter which one) to calculate the Power Spectral Density of a signal. For example say I want to use the hann window, with $N = 1024$,...
4
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2answers
6k views

What should be the correct scaling for PSD calculation using $\tt fft$

I would to calculate the PSD of a signal using FFT however the result do not match with periodogram command. What did was as follow : ...
11
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3answers
4k views

Shift a signal by fraction of a sample

I have a signal with a sample time of 0.5 micro seconds and I would like to shift this signal by a fraction of the sample time, say by 3 nano seconds. I have read a few online resources about ...
4
votes
4answers
632 views

Why do we have to rearrange a vector and shift the zero point to the first index, in preparation for an FFT?

I am trying to learn how to implement the FFT as a way to approximate the continuous-time Fourier transform, and as a "nice easy example" I have chosen to test it with a simple Gaussian pulse in the ...
3
votes
1answer
441 views

why do we use $X(e^{j\omega})$ instead of $X(j\omega) $ in Discrete Time FT

I am studying DT-FT. But I cannot figure out why we use $X(e^{j\omega})$ instead of $ X(j\omega) $ in DT FT Thanks in advance..
1
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2answers
219 views

What is meant by *sampling* in terms of the *sampling theorem*?

Let $y:\left(-\frac T2,\frac T2\right)\to\mathbb{C}$ be a square integrable function. The Fourier coefficients of $y$ are $$\underline{Y}(k):=\frac 1T\int_{-T/2}^{T/2}y(t)e^{-i\omega_kt}\;dt\;\;\;\...
0
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1answer
507 views

understanding discrete-time convolution in LTI systems

I'm trying to understand the discrete-time convolution for LTIs and its graphical representation. standard explanations (like: this one) start with the idea of decomposing an input signal $x[t]$ into ...
14
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7answers
13k views

Why Does the DFT Assume the Transformed Signal Is Periodic?

In many signal processing books, it is claimed that the DFT assumes the transformed signal to be periodic (and that this is the reason why spectral leakage for example may occur). Now, if you look at ...
27
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2answers
4k views

Are there alternatives to the bilinear transform?

When designing a digital filter based on an analog filter we usually use the bilinear transform. To approximate a discrete transfer function $D_a(z)$ from analog (continuous) transfer function $A(s)$ ...
8
votes
2answers
3k views

How can output sequence be equal to the sum of copies of the impulse response, scaled and time-shifted signals?

I am sorry, this is a very basic question. But i am having hard time understanding is how it is possible. I know impulse response is the output of the system when impulse sequence is given as input ...
7
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1answer
3k views

Magnitude-squared Coherence calculation inconsistence

I have to calculate the magnitude-squared coherence (MSC) between two signal. However, using a routine that uses only one taper (or no tapers at all) my result is always 1, despite the signals are ...
13
votes
2answers
6k views

Discrete-time Fourier Transform of the unit step sequence $u[n]$

From text books we know that the DTFT of $u[n]$ is given by $$U(\omega)=\pi\delta(\omega)+\frac{1}{1-e^{-j\omega}},\qquad -\pi\le\omega <\pi\tag{1}$$ However, I haven't seen a DSP textbook that ...
12
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3answers
6k views

How to detect “fast” changes in signal processing

I'm working on a project where we measure the solderability of components. The measured signal is noisy. We need to process the signal in real time so that we are able to recognize the change that ...
9
votes
1answer
4k views

Scalogram (and related nomenclatures) for DWT?

My understanding of the scalogram is that, for a particular row, the scores of the projection of the input signal with the wavelet at a particular displacement is shown. Across rows, the same thing ...
5
votes
1answer
2k views

How do I convert a real baseband signal to a complex baseband signal?

I have radio telescope observations that have resulted in two real-valued signals (corresponding to the right- and left-handed circular polarizations). The signals are sampled at rate $2B$, and ...
3
votes
3answers
2k views

Measure Sine Wave Amplitude from ADC Signal

Question I'm trying to do some DSP that I have never done before and a nudge into the right direction would come in handy. The context is replication of this project. The system architecture is the ...
3
votes
2answers
394 views

Quadrature modulation

I have a question: What is the difference between $ I \cos(t) - Q \sin(t) $ and $ I \cos(t) + Q \sin(t) $ except that they are phase shifted 90 degrees ? On the internet I can find both ...
6
votes
3answers
9k views

RMS calculation in frequency domain after windowing

I can calculate RMS in frequency domain as derived from Parseval's Theorem. But what if I have applied a windowing function before doing the FFT (in my case a Hann window)?. Now the RMS values are ...
5
votes
8answers
270 views

How Do I Measure the Time Duration of a Finite Length Discrete Sequence?

Assume I have a five-sample time-domain sequence (none of the five samples are zero valued) and the time period between each pair of samples is one second. Measured in seconds, what is the time ...
2
votes
2answers
887 views

Linear and Circular Convolution in Fourier Domain (DFT)

Suppose we have two vectors A and B of length 100 and 80 obtained as a function of time. If we wish to perform convolution of the two vectors in the Fourier domain, we need to multiply the Fourier ...
0
votes
2answers
510 views

my Butterworth lowpass formulas do not agree with Fisher webpage

I want to implement Butterworth low-pass filter. Thanks to this question, I have found out that the filter coefficients can be generated using Tony Fisher web-site or using his code. But the problem ...
5
votes
4answers
7k views

Calculate Phase angle between two signals i.e. digital Phase meter

I want to calculate the phase difference between the two channels(signals) of a stereo audio file.(uncompressed data i.e. PCM samples). I want to determine whether whether two signals are in phase or ...
1
vote
2answers
340 views

Output of a discrete-time LTI system different form than input?

This question is related to this one. I'm going through old exams for a 2nd year systems and transforms course, and came across this question. I'm posting this question just in case my other question ...
1
vote
2answers
2k views

What is a memory less system?

As far as I have grasped the concept is that if we are given the expression $$y[n]=(2x[n]-x^2[n])^2\,,$$ it is a memory less system because even if we give negative values of $n$, we still get the ...
0
votes
1answer
642 views

Upsampling and comb function

Could somebody explain how upsampling works with comb function. How comb function looks for upsampling process? (if it possible I would appreciate if answer would be related to DFT)
8
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3answers
2k views

Mathematically Inclined Signal and Systems / Signal Processing Book Recommendations

I'm an electronics engineering student with high inclination to analysis and pure mathematics. I was just wondering if there was any book ( or any resource ) that treats signal and systems and signal ...
9
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2answers
2k views

What kind of filter is that? Is it IIR?

I am trying to answer the following question: Is the system described by equation: $$y[n]=0.5y[n-1]+x[n]-0.5x[n-1]$$ an IIR filter? My answer is yes. Thank you
10
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3answers
1k views

Is there a way to obtain the impulse response of a discrete system by just knowing it's response to the discrete unit step function?

In continuous time it was possible; $$ u(t){\longrightarrow} \boxed{\quad\textrm{system}\quad} {\longrightarrow} y(t)\implies \delta(t)=\frac{du(t)}{dt}{\longrightarrow}\boxed{\quad\textrm{system}\...
11
votes
1answer
245 views

Quantitative Comparison of Scaled, Delayed and Warped Signals

The following question is detailed in 1D, with time as the ordinal variable. Similar questions could apply in other dimensions. In several signal processing techniques, such as blind source ...
2
votes
2answers
21k views

What is the difference between continuous, discrete, analog and digital signal?

It's my first time studying DSP and I've faced a problem finding a convenient definition. Are the following definitions correct? And if so why there are some resources defining it in other terms such ...
15
votes
1answer
8k views

Getting loudness of a track with RMS

I'm trying to calculate the loudness of an audio track I have stored in a buffer. The buffer contains PCM data of the signal and I want to get how 'loud' it is by using Root Mean Squared. I assume I ...
6
votes
2answers
7k views

The difference between DFT and DFS

In the literature, I've found that DFS and DFT are one and the same. If they are one and the same why to use two different names for them? If there is really a difference what is it and what is the ...

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