13 votes

Compensating Loudspeaker frequency response in an audio signal

Yes, you can do this with an LMS equalizer which uses the Wiener-Hopf equation to determine the least squared solution to the filter that would compensate for your channel, using the known transmit ...
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  • 37.7k
12 votes
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Why don't unit circle poles lead to infinite amplitude response for Butterworth lowpass?

You've made an understandable mistake. You are probably looking at this picture: That is not the unit circle, and it isn't even in the $z$ domain. What you are looking at is the locations of the ...
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  • 8,646
11 votes
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This is how my professor is finding the frequency response of an LTI system when given the impulse response. Is this wrong?

Your professor is right, and you're almost right too. The filter is clearly an FIR filter, but because its frequency response can be expressed as a geometric series, a recursive implementation is ...
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  • 80.4k
9 votes

Can two different impulse responses give the same frequency response?

No. The impulse response and frequency response of an LTI system are related by the Fourier transform, which is one-to-one.
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  • 23.7k
8 votes
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Design a linear-phase FIR filter approximating the magnitude of a given IIR filter

What you do in step 1 is simply truncate the infinite impulse response to approximate it by an FIR filter. If you use sufficiently many filter taps, the approximation becomes arbitrarily accurate. ...
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  • 80.4k
7 votes
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Understanding the $\mathcal Z$-transform

Consider a liner discrete-time system. Assume we can define it in terms of an input-output relation as follows (you can assume a more general model but it is enough for our purpose): $$a_0y[n]+a_{1}y[...
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  • 4,115
7 votes
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Why zeroes near the unit circle cause a dip in frequency response, while poles cause a peak?

To answer this you need to understand what is a pole and what is a zero of a transfer function. Let's look at a simple 2 poles 2 zeros filter (also called biquad filter) transfer function : $$ H(z) = ...
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  • 664
7 votes
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why exponential term neglected in equation?

The magnitude of that complex exponential is 1. Recall from complex algebra: any complex number can be expressed as $z = r e^{j \phi}$ where $|z|=r$ is its magnitude and $\arg z = \phi$ is the ...
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  • 4,014
6 votes

Berchin's FDLS arbitrary filter design algorithm

FDLS requires a causal frequency response. Your prototype frequency response has zero phase everywhere, which is most definitely not causal. An IIR filter order of 50 is humongous. When FDLS has too ...
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6 votes

System response: LTI system for $x[n] = \sin(\frac{\pi n}{4})$

You're definitely on the right track. The way you're trying to solve the problem is the best and simplest. You just need to realize that you need to evaluate the magnitude and phase of the frequency ...
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  • 80.4k
6 votes

Can two different impulse responses give the same frequency response?

To add on to what has been said, what you're asking is, if you have $h_1$ and $h_2$ as impulse responses of a LTI systems (continuous-time or discrete time) and $H_1$, $H_2$ their respective frequency ...
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  • 3,272
6 votes

Design of a digital A-weighting filter with arbitrary sample rate

It's a common misconception that the approximation of an analog filter by a digital filter must be bad close to Nyquist. This idea might come from the ubiquity of the bilinear transform, for which ...
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  • 80.4k
6 votes

For 2D signals can it be said that the frequency response is the same as the Fourier transform?

Yes for 2D signals you can take a 2D fft, and if the 2D signal is represented in the time domain, then its fft is represented in the frequency domain. 2D FFT's have many other interesting ...
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  • 37.7k
6 votes
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Why the frequency response plots (of causal filters) only show positive frequency?

This has absolutely nothing to do with causality. The frequency response of a real-valued filter (i.e., one with a real-valued impulse response) is (conjugate) symmetric, i.e., the negative ...
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  • 80.4k
5 votes

Approximate a System Frequency Response with a Filter in MATLAB

Convolve the input signal with (Real Part) harmonic signal $ \alpha {e}^{-2 \pi i {f}_{0} t + \phi} $. Let's call this output as $ {y}_{1} $. The parameters $ \alpha $ and $ \phi $ are from your ...
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  • 41.4k
5 votes

For an LTI system, why does the Fourier transform of the impulse response give the frequency response?

The intuitive answer is that an impulse in time at t=0 contains all frequencies of equal magnitude, so applying an impulse to an LTI system is the same as applying all frequencies at once, thus the ...
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5 votes

How frequency response related to a transfer function

An LTI system's "frequency response" tells you how the system acts on the amplitude and phase of a sinusoidal input. If the frequency response is $H(f)$, then an input $x(t)=e^{j2\pi f_0t}$ produces ...
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  • 13.8k
5 votes
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Lagrange Multipliers Optimization - Complex Functions

I found the following in Charles Therrien's "Discrete Random Signals and Statistical Signal Processing" in one of the Appendicies. Say you have the function $Q(a)$ you wish to minimize such that $C(a)...
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5 votes
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Why must I take abs of filter frequency response?

Frequency response has two parts: amplitude response and the phase response. Both of these are represented as a complex signal when you get the response from freqz. ...
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  • 4,115
5 votes
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calculating DC value from positive frequency with its DC undefined

Assume you have the signal $$x(t)=a+b\cos(\omega_0t)\tag{1}$$ with some non-zero real-valued constants $a$ and $b$. Now remove DC and the negative frequencies to obtain $$x'(t)=\frac{b}{2}e^{j\...
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  • 80.4k
5 votes
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What is the time unit of the converted Channel Impulse Response?

Because you don't have background in wireless communications, I will try to answer as simply as possible. What is the time unit of the converted CIR? Just time unit. It can be second, ms, us, etc. ...
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  • 5,780
5 votes
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Simplifying frequency response equation

$$1 - e^{-4j\omega} = e^{-2j\omega}(e^{2j\omega} - e^{-2j\omega}) \tag{1}$$ Now, $$ \sin(2\omega) = \frac{e^{2j\omega} - e^{-2j\omega}}{2j} \tag{2}$$ Equation 2 is a consequence of Euler's ...
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  • 2,552
5 votes

Calculating the 3dB frequency of an nth order low pass filter and nth order high pass filter

In general there is no straightforward analytical solution. As you know, you need to solve $$\left|H(e^{j\omega_c})\right|=\frac{1}{\sqrt{2}}\tag{1}$$ for $\omega_c$, where it is assumed that the ...
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  • 80.4k
5 votes
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Correcting phase response of a signal

You can equalize magnitude and phase simultaneously by defining a desired complex frequency response $$D(\omega)=M(\omega)e^{j\phi(\omega)}\tag{1}$$ with magnitude $M(\omega)$ and phase $\phi(\omega)$ ...
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  • 80.4k
4 votes
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Measuring frequency response range of piezoelectric disc

I am afraid that it is rather impossible without a proper hardware. Sweep sine is ok as a general method, but you would either need: Reference transducer with known (preferably) linear frequency ...
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  • 10.5k
4 votes
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Difference between $\tt freqz()$ and $\tt plot(abs(fft()))$ in MATLAB

You calculating FFT only from two samples. You need to pad your impulse response with zeros to get a valid result. So in MATLAB that would be: ...
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  • 10.5k
4 votes
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Calculation frequency response of digital filter with known structure

For the given system you can write down the input-output relation as $$y[k]=\frac14\left(x[k]+2x[k-1]+x[k-2]\right)\tag{1}$$ because $T$ (or $z^{-1}$) denotes a delay element, which delays its input ...
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  • 80.4k
4 votes
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How to stabilize a filter

The magnitude of the frequency response will remain unchanged if you reflect any poles outside the unit circle - these are the ones causing instability - back inside the circle. I.e., a pole $p$ (with ...
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  • 80.4k
4 votes
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From lowpass to bandpass

You just shifted the low pass filter to the right, so you generated a complex-valued filter, as you've observed. Multiplying a real-valued impulse response with a complex exponential naturally results ...
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  • 80.4k
4 votes
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Is the book wrong? -- How to sketch frequency response obtained from H(z)?

As far as I can tell, the book is not wrong. (By the way, you're studying a 3-point moving average filter here, and it's useful to know about such filters.) Your 1st question: That center dot on the ...
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