10 votes

Signal processing in Python vs C++ (band-pass filter)

Not really an answer but too long for a comment. Standard software development and debug techniques should solve this Don't use code on real data before it has passed all unit tests First write the ...
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  • 32.5k
9 votes

Simple and Effective Method to Estimate the Frequency of a Single Sine Signal in White Noise

I assume the model to be: $$ x \left[ n \right] = \sin \left[ 2 \pi \frac{f}{ {f}_{s} } n + \phi \right] + w \left[ n \right] $$ Where $ w \left[ n \right] $ is white noise uncorrelated with the ...
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  • 41.2k
7 votes

Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

Consider the identity system $y(t) = x(t)$. This system is LTI. If the input $x(t)$ is discontinuous, then the output $y(t)$ will be discontinuous too.
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  • 13.8k
7 votes

Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

To add an even worse example to MBaz (best possible) counterexample: The derivative $\frac{\mathrm d}{\mathrm dt}$ is an LTI system. $f(t)=|t|$ is a continuous function. $\frac{\mathrm d}{\mathrm dt}(|...
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6 votes

Detect a Frequency Change in a Step Wise Frequency Chirp

There are many way to tackle this: Time - Frequency Analysis Classic choice would be a spectrogram but probably a Fourier Synchrosqueezed Transform would do a better job (Have a look at even more ...
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6 votes
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Is it possible to calculate a 48-point FFT using a 32-point FFT and 16-point FFT?

If not, what is the most efficient way of implementing a 48 point FFT? Three 16 point FFTs plus one set of 3 point "Butterflies". Matlab example ...
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  • 32.5k
5 votes

Confusions regarding differences between Fourier transform & Laplace transform?

Concerning your first question, both, the Laplace and the Fourier transform, are frequency domain representations of a function or signal. In the Fourier transform we deal with a real-valued frequency ...
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  • 80.4k
5 votes
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Analysis of two audio signal by autocorrelation

The "MCU" plot looks like there was a DC component in the signal, that ran through the autocorrelation function. The triangle is typical for this. Try highpass filtering before the analysis. ...
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  • 1,872
4 votes
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Baseband and Passband signals

No, there is no standard way to represent a complex passband signal in baseband. However, this is not often a problem, at least in communications, because most passband signals of interest are real (...
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4 votes
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How to alleviate the edging effect of the Hilbert transform?

The effect can be alleviated with appropriate padding, which imposes a 'statistical prior' (i.e. assumption). No padding is equivalent to periodic padding, meaning signal's right joins its left, and ...
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4 votes
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Premier Signal Processing conference

IEEE ICASSP is probably still the largest international conference on communications and signal processing. IEEE Transactions on Signal Processing and Communications are well-regarded journals.
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4 votes

does T = 1/F always hold?

To understand sampling and aliasing I think a useful analogy is a strobe light on a bicycle wheel. The rate of rotation of the bicycle wheel in revolutions per second represents the frequency of an ...
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  • 37.6k
4 votes
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Are the output functions of a continuous-time LTI system necessarily continuous (in the calculus sense) for any given input functions?

The tag continuous-functions made me interpret the question a bit differently, as nice and simple counter-examples have been given. I consider here that a system is ...
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4 votes
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Why signal add noise cause signal undiscoverable after `fft` and `ifft`?

You want to just do signal + noise, and you'll be fine for the noise part. For the plot, you need the absolute of the fft, you're just plotting the real part. ...
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4 votes

The Amplitude of the Correlation Function Peaks After Matched Filtering

Without any restrictions on $ h $ you may build some very non real world cases. Especially if we're talking about the correlation function without the removal of the DC component. For instance, think ...
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4 votes
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What is the relationship among digital filter cutoff frequency, signal frequency and filter settling time?

With "Settling Time" we can consider the overall time delay of the filter, and the rise/fall time of a transient change going through the filter. The rise/fall time will inversely related to ...
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  • 37.6k
4 votes
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Crash course on Sonar

The two main books that I've seen most often are: Richard Neilsen - Sonar Signal Processing see here which covers: Beamforming, LOFAR, DEMON processing, active and passive systems. William Burdic - ...
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3 votes
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What algorithm can I use to compare two signals' similarity?

Instead of using the raw gyroscope measurements, I would recommend processing/converting the raw measurements into roll, pitch, and yaw angles. Conversion helps with the interpretation. You can try ...
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  • 406
3 votes
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Comparing distribution of vectors with different length?

From what you've said, you have two sample sets: $$x_n, n = 0 \ldots N-1$$ and $$y_m, m = 0 \ldots M-1$$ where $M \ne N$ and you want to compare the distributions of the underlying processes. Do you ...
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  • 22.9k
3 votes
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Integration of Sinusoidal functions

Yes and no. If you recall from Calculus, if $g(t) = \frac{d}{dt} f(t)$, then $\int g(t)\ dt = f(t) + C$. So, since the derivative of a sinusoid is a sinusoid of the same frequency, if $g(t)$ ...
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  • 8,610
3 votes
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Trouble understanding how image digitization works

The image in a digital camera/sensor is represented as a matrix of discrete numbers, as you say. The (spatial) digitization consists of an array of sensels each with some non-zero area that are ...
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  • 2,264
3 votes

Finding the mode of propagation of a progressive wave and the velocity of that mode

In your case the wave number $k = 2\pi f/c=2\pi$, $k_x$ and $k_y$ should satisfy $$ k^2 = k_x^2+k_y^2 $$ which means they are not always real. But the direction of propagation of wave is easy to ...
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  • 2,628
3 votes

Finding the mode of propagation of a progressive wave and the velocity of that mode

As already commented so far, for the linear wave equation to be satisfied in any number of dimensions the condition (here shown for three dimensions) $$ k^{2} = k_{x}^{2} + k_{y}^{2} + k_{z}^{2}$$ ...
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  • 742
3 votes
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Methods to increase FFT time resolution without lowering FFT size

Yes. Windowing will decrease the frequency resolution and therefore increase time resolution. The resolution bandwidth as the inverse of time resolution is well tabulated in the classic paper by fred ...
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  • 37.6k
3 votes
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About the process to convert basedband signal into passband

In order for $x(t)$ as a passband signal to be equivalent to a complex signal, it must be a passband signal. The example the OP gave is ultimately multiplying by a constant, which is DC, which is a ...
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  • 37.6k
3 votes
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How to choose correctly oversampling ratio?

The referenced post does not imply that 8 samples per symbol are required, that is only what was used in order to show the extended spectrum as copied below: What I have also included in this copy of ...
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3 votes
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What is the complexity of multiplication a real matrix with real vector

If you multiply an $M \times N$ matrix with an $N \times 1$ vector you get a vector of size $M \times 1$ For the generic case you will need $M \cdot N$ multiplications and $M \cdot (N-1)$ additions. ...
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  • 32.5k
3 votes

What is the relationship among digital filter cutoff frequency, signal frequency and filter settling time?

(1) Filter settles slower if the ratio between signal frequency and filter cutoff frequency is smaller; (2) Filter settles slower if bandwidth of a band-pass filter is narrower: Correct in the sense ...
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  • 32.5k
2 votes

Down sampling an EEG signal

Merely downsampling will result in a loss of information, unless you know the data of interest lives in a particular frequency band which you can filter down to. To determine that, you should look at ...
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  • 598
2 votes

How does the Hilbert Transform extract the in-phase and quadrature phase components of a real passband signal?

First a definition: an analytic signal is one who's negative frequency components are zero. For a real signal $x(t)$, the Hilbert transform computes the imaginary component of the corresponding ...
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