# Tag Info

Accepted

### What would be the effect of repeating samples in time domain on frequency domain?

It's quite beneficial to view the mathematical expression of the process as well. A mere $N$ times repetition of a single sample (pixel) into the new enlarged block is an interpolation with zero-order ...
• 28.3k

### What’s a good book on multi-rate dsp?

Assuming you have completed the basic course in DSP with a book like Oppenheim's Discrete-Time Signal Processing book then the next step could be anyone of the followings: Multiresolution Signal ...
• 2,620
Accepted

### Reversing the order of up and downsampling

The problem with downsampling is that it can be lossy -- since you're reducing the sampling rate, you can introduce aliasing. So, you can reverse the order whenever downsampling does not result in ...
• 15.3k
Accepted

### Room Impulse Response Domain of Sparsity

That's tricky. RIRs are NOT sparse in any obvious physical sense (time, frequency, etc). In fact they are insanely complicated with thousands of degrees of freedom. The amount of relevant physical ...
• 45.6k

### Upsampling with time offsets

Answer: You will see residual images of $X(f)$ at multiples $f_s$, $2f_s$ and $3f_s$, and distorted image of $X(f)$ at non-zero multiples of $4f_s$, when sampling in the manner you explained. ...
• 2,611

### What would be the effect of repeating samples in time domain on frequency domain?

There are two ways (I see right now) to model this system in terms of other known systems. First that comes to my mind is a zero-order sample and hold system. Although those are usually described in a ...
• 231

### Advantage of complex filtering in multirate applications

For one practical example, I'll point to GNURadio's frequency translating FIR filter block: https://github.com/gnuradio/gnuradio/blob/master/gr-filter/lib/freq_xlating_fir_filter_XXX_impl.cc.t It's a ...
• 2,710
Accepted

### Use polyphase representation to construct a perfect reconstruction filter bank

This is a problem from Multirate Systems and Filter Banks by P. P. Vaidyanathan. In Section 4.6.2.E, there is a discussion on what he calls Euclidean Complementary Functions. Specifically, he ...
• 46
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### Why do Dyadic filterbanks downsample the high pass signal portions?

[Good question, that made me rethink of stuff I believed natural. I shall incorporate them in future lectures] Downsampling the highpass (and the lowpass) provide you with a critically sampled ...

### Recovering a signal that was upsampled by non-integer factor

The Sampling operation (both upsample and downsample) depends on two very critical conditions: 1- The existance and applicability of ideal frequency selective filters 2- The operated signal being ...
• 28.3k
Accepted

### With regards to multirate processing, what are the benefits of having a 'slower' sampled signal?

In addition to what hotpaw2 said, it's important to understand that sample rate reduction is the corner stone of actual applicability in many systems. Software Defined Radio frontends nowadays ...
• 31.3k
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### Confusion in FFT of Resampled Data

As you know you have to use an ideal low-pass filter, and zero order hold is an approximation which needs more compensation. Ideal LPF has a flat response with sudden cut-off and zero stop band but ...
• 1,327

### Understanding sampling rate conversion

You would upsample by 441 and downsample by 640 since $11025 \cdot 640 = 16000 \cdot 441$ That would be a rather expensive operation, so in practice you would either fugde it a bit: 31/45 would get ...
• 45.6k

### Decimator effect on wide sense stationary input

The decimator by integer $M$ can be shown to be the following block: $$x[n] \longrightarrow \boxed{ \downarrow M } \longrightarrow y[n] = x[Mn]$$ Assuming that the input $x[n]$ is WSS it has the ...
• 28.3k

### Drawbacks of upsampling using polynomial interpolation

Linear and more generally polynomials are pretty common methods for interpolation or extrapolation, easy to implement, and simple in a causal setting (prediction). Parabolic interpolation (in the ...

### Getting error while performing upsampling of an audio signal processing using low pass filter in python

This code seems to do what you're asking for. ...
• 25.9k
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### Multirate Control System Transfer Functions

The primary impact of a CIC filter in a control loop is the delay it introduces, as a linear phase filter, in addition the change in amplitude within the loop bandwidth. The gain reduction actually ...
• 52.3k
1 vote

### Drawbacks of upsampling using polynomial interpolation

If you are upsampling a class of bandlimited signals, such as specch, using polynomial interpolators, then you are introducing erros into your results. This is because polynomial interpolators will ...
• 28.3k
1 vote
Accepted

### Polyphase components Spectrum formula in Discrete time

Let's start with your equation. $$P_k\left( e^{j\Omega} \right) = \frac{1}{L} e^{jk\Omega/L} \sum_{p=0}^{L-1} e^{-2 \pi j k p / L} H\left( e^{j(\Omega-2\pi p)/L} \right)$$ Do a little rearranging....
• 7,590
1 vote
Accepted

### What does it mean for a Wavelet transform to commute with translations?

We can start from what is "shift invarient": Transform G is shift invariant if - $$\forall x:\sigma^nG(x) = G(x)$$ $\sigma^n$ being shift by n. Examples for transforms that are invarient to shifts ...
• 471
1 vote

### Polyphase Analysis Filter Bank

With every polyphase filter bank I have worked with, the first block in the analysis phase is an IFFT, and the block in the synthesis phase is a DFT. These operations essentially cancel one other, so ...
• 863
1 vote

### Decimator effect on wide sense stationary input

just a WSS signal $x[n]$ passed through an $M$-fold decimator (a multirate signal processing block where $M=2$, used in fractional rate conversion), no filter follows the decimator. So $y[n] = x[Mn]$ ...
• 31.3k
1 vote

### Unscented Kalman Filter - Multiple Consecutive Measurement Updates

@Royi's and user28715's answers are correct. So just add this answer to theirs. If you let the system's output matrix $H$ go to zero, then two things happen. First, you are modeling a time increment ...
• 12.9k
1 vote
Accepted

### Unscented Kalman Filter - Multiple Consecutive Measurement Updates

I will use Wikipedia notations - Kalman Filter. In most models the state transition model matrix $F$ depends on the interval parameter $T$. The same goes for the Process Noise Covarinace Matrix \$ ...
• 19.8k
1 vote

### How to undo dynamic Doppler effect by software?

If the only reason for the buffer is so your algorithm has something to process, then the simplest way to implement this is to keep your current algorithm but use a shorter buffer. If the larger ...
• 279
1 vote

### Multirate Signal processing for matching DAC of the SDR

25.6 MHz is larger than the largest possible sampling rate of these two USRP models (25MHz). Therefore, this is impossible to implement directly; in any way, you'll need to generate your 25.6 MS/s ...
• 31.3k
1 vote

### Extracting narrow-band ZigBee signals(4 MHz) from a wide-band WiFi signal(20 MHz)?

Put band pass filters (5 MHz wide) … Re-sample the chunks to 4 MHz. Don't do that! If you reduce the sampling rate to 4 MS/s, you need to filter to 4 MHz bandwidth anyway. So you could instead just ...
• 31.3k
1 vote

### With regards to multirate processing, what are the benefits of having a 'slower' sampled signal?

Once upon a time, when a lot of DSP algorithms were being developed, expensive DSP processors were a thousand to maybe a million times slower than a current budget smart phone. Same issue with memory ...
• 35.4k
1 vote

### Recovering a signal that was upsampled by non-integer factor

The matlab functions upsample and downsample just insert zeros, and remove samples respectively. There are big aliasing/imaging ...
• 111

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