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Alias frequency Formula

One easy formula: $$ f_{a} = \text{sign}(f) \; \cdot \; \left( |f| - \Big \lfloor \frac{|f|}{f_{\text{nyq}}} \Big\rfloor \; \cdot \; f_{\text{nyq}} \right) $$ where $f_{a}$ is the aliased frequency, ...
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How do you find the null to null bandwidth for the signal below?

The $\text{sinc}$ function is the Fourier Transform of a Rectangular pulse. Its zeros are located at non-zero integers of $x$. Therefore, if your spectrum can be expressed as $\text{sinc}(Bx)$, the ...
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0 votes

How do you find the null to null bandwidth for the signal below?

The key observation is that $\text{sinc}(x)$ is zero for all arguments $x$ that are nonzero integers, so the problem reduces to "what values of $f$ yield the nonzero integers closest to zero, ...
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How do you find the null to null bandwidth for the signal below?

The following MATLAB script is a solution to your question clear all;close all;clc 1. fzero only returns 1 zero ...
1 vote

What are some approaches / algorithms for reducing size of numerical data of large size with redundancies?

You have two issues here: Number 1: your format is very inefficient. If you convert this from Ascii to a suitable binary format, you can probably reduce the size by a factor of 4 or so. Number 2: your ...
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1 vote

What are some approaches / algorithms for reducing size of numerical data of large size with redundancies?

What makes this dataset so big is not per se the number of samples. In your case, it's the ASCII format*. You should just convert the data to 32bit (or even just 16bit or lower, depends on the ...
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1 vote

Algorithm to detect down-up-down pattern in time series

Step 1: Low Pass Filter Step 2: 2nd derivative. The 2nd derivative gives you the curvature. Step 3: If it switches sign three times, check the values at those points to confirm they're actual peaks. ...
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1 vote

Algorithm to detect down-up-down pattern in time series

Can you narrow down how the plot should generalize? Ie how much variation do you expect for the time between edges and absolute step height? What might noise (variable stuff that should lead to no ...
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2 votes

Algorithm to detect down-up-down pattern in time series

Very first thought here: Aggressive Low Pass (to get the trend, would be a pretty low cut-off you can experiment with). Local maxima and minima detection (you can use the 1st derivative's 0-crossings ...
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3 votes
Accepted

Different PI controller implementations and their respective discrete transfer functions

On the 2nd approach, your transfer function looks fine but translating it into C code appears wrong. To re-write your z-domain as a discrete finite difference equation where $y$ is the output and $a=...
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2 votes

Transfer function and Laplace domain

(I was going to leave @Matt L.'s answer but, given the line of comments, I'll try, too) Let's say you have a 1st order lowpass prototype and you feed it a sine: $$\begin{align} &H(s)=\dfrac{1}{s+1}...
2 votes

Transfer function and Laplace domain

First of all it's important to understand that this is all about linear and time-invariant (LTI) systems. Otherwise, you can't generally use a transfer function to characterize a system. So if you ...
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2 votes
Accepted

Name of property of Laplace transform

That's the Frequency Shifting Property
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2 votes

Why do we decompose signals to even and odd

Following Robert's answer, decomposing a (complicated) function into a combination of (simpler) functions is useful in many cases. Here "simpler" is related to showing more symmetry: an even ...
2 votes

Why do we decompose signals to even and odd

Assuming $x(t)$ is purely real, and also the even and odd components, one reason is that the Fourier Transform of an even function is purely real and has even symmetry. And the Fourier Transform of ...
1 vote
Accepted

How do I determine if the fundamental period $T_{x}$ exists and if so what it is?

Your almost there. Let's pick it up at $$T_{x} = xT_{a} = yT_{b} = zT_{c} = \frac{x\pi}{3} = \frac{y\pi}{4} = z\pi$$ The key here is that $x,y,z \in \mathbb{I}$ must be integers. Let's pull out $\frac{...
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1 vote

How do I determine if the fundamental period $T_{x}$ exists and if so what it is?

All (finite-energy) periodic signals can be represented by Fourier series which consist of a sum of harmonics of a fundamental frequency $\omega_0$. Some of the various harmonics as well as the ...

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