# Tag Info

### 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 ...
• 37.7k
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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 ...
• 8,646
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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 ...
• 80.4k

### 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.
• 23.7k
Accepted

### 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. ...
• 80.4k
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• 664
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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 ...
• 4,014

### 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 ...
• 124

### 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 ...
• 80.4k

### 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 ...
• 3,272

### 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 ...
• 80.4k

### 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 ...
• 37.7k
Accepted

### 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 ...
• 80.4k

### 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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### 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 ...

### 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 ...
• 13.8k
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• 80.4k
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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 ...
• 80.4k