jithin
  • Member for 4 years, 11 months
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  • Bangalore, Karnataka, India
3 answers
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1k views
Understanding the Difference Between MAP Estimation and ML Estimation
6 votes

You have a set of message set $m_i$, $0 \le i \le N-1$. (For example, QPSK will be $N=4$). For the transmitted message $m_i$, the corresponding symbol vector is $\textbf{x}_i$, and the received symbol ...

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192 views
Circular Convolution and FFT of power 2
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4 votes

Circular convolution is just linear convolution aliased by DFT length $n$. The length of linear convolution of $a$ and $b$ will be $2n-1$. So take $FFTs$ of $a$ and $b$ , padding each of them to ...

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3 answers
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413 views
How do you sub-sample an FFT?
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4 votes

it seems like the bigger problem is that subsampling the signal would result in aliasing frequencies No, subsampling in frequency domain corresponds to aliasing in time domain. So the idea here is to ...

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2 answers
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183 views
OFDM time vs. frequency domain channel estimation/equalization
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4 votes

Traditionally, OFDM became popular in WiFi and LTE because the channel model consisted of multi-path. That is, the radio signal transmitted in 1-6GHz frequencies bounced from various obstacles (walls, ...

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2 answers
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152 views
Why Convolve instead of Cross-Correlate for Detection of Known Signal?
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3 votes

Convolving with Matched Filter is same as cross-correlation. Suppose say your known signal is $x[n]$ for $0 \le n \le N-1$. The matched filter is $$ h[n] = x^*[N-n] $$ where $*$ denotes conjugate (...

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4 answers
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845 views
How to derive the bin width / maximum frequency of DFT/STFT
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3 votes

But I want to see why either the bin width is 1/T where T is the duration the samples are taken over, or why the DTF is Fs Hz periodic. (I think bin width as Fs/N is a red herring) The fourier ...

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2 answers
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454 views
Relationship between Nyquist and Shannon channel capacity
2 votes

Well, I think both are unrelated unless you have some constraints. The Nyquist channel capacity says you can transmit $2B\log_2(M)$ bits per second for given channel bandwidth $B$. It does not say ...

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3 answers
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127 views
For Schwarz inequality for 2 signals $s_1(t)$ and $s_2(t)$, equality holds if $s_1(t) = c\cdot s_2(t)$ ($c$ is constant). Does $c$ have to be real?
2 votes

$c$ need not be real number. For the LHS you would get $$ |\langle s_1,s_2\rangle| = |\langle s_1,cs_1\rangle |=|c|\,|\langle s_1,s_1\rangle |= |c|\|s_1\|^2 $$ For RHS, $$ \|s_1\| \times \|c s_1\| =\...

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187 views
Why multi-path channel has linear phase within the coherence bandwidth?
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2 votes

For the classical baseband channel model for multipath, $h(t)=\sum_ka_k\delta(t-\tau_k)$, the frequency response $H(f)=\sum_k a_ke^{-j2\pi f\tau_k}$. If $K=1$, single tap the phase would have been ...

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164 views
Calculating Cross Power Spectral density between two complex signals
2 votes

Cross correlation is defined as $R_{xy}(\tau) = E\{x(t)y^*(t+\tau)\}$. You missed to take the conjugate of $x_2$. So $x_1x_2^* = (c+id)(a-ib) = ac+bd +i(ad-bc)$. Cross PSD is the fourier transform of ...

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361 views
Effect of changing sample rate, window duration and zero padding on DTFT and DFT
2 votes

halving the $F_s$ (keeping $T$ and $N$ constant) would remove the right half of the bins (halving the maximum frequency) No. Number of bins remain same because you have not changed $N$. What will ...

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2 answers
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71 views
How can I shape my time channel response, in order to have Gaussian shaped Doppler Spread?
2 votes

See section 2.4.3 of this reference https://web.stanford.edu/~dntse/Chapters_PDF/Fundamentals_Wireless_Communication_chapter2.pdf If the doppler spectrum has to be gaussian, the auto-correlation of ...

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136 views
Discrete and Continuous Signals
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2 votes

Your understanding is correct and you can apply Hann windowing on discrete signals. The choice of your window depends on how easily you can visually resolve two sinusoids that are closely spaced in ...

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468 views
Visualizing the "frequency shift" theorem in FFT
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2 votes

In the line Inverse_GShifted=real(ifft(GShifted)); I have changed to Inverse_GShifted=real(fftshift(ifft(GShifted))); This is because the ifft output is from $0 \le n \le N-1$, but your actual ...

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94 views
Rectify signal basic question
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2 votes

The only reason I can think of may be to preserve the frequencies over which original signal had spectrum (before squaring). When you square a signal $x[n]$, whose spectrum $X(e^{j\omega})$ extends ...

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152 views
Why is the error between the desired signal and estimated signal in the case of LMS filter remaining constant even after n number of iterations
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2 votes

As mentioned in the comment, I modified the code given here and was able to adapt the LMS filter with error tapering to zero. The only assumption I made is that (since I am not an audio expert and do ...

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170 views
What's the computational complexity of MMSE equalizer in OFDM system
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1 votes

For a SISO channel, assuming you have estimated channel coefficients for each sub-carrier $k$, the MMSE equalizer is $$ \hat{h}_k=\frac{h_k^*}{|h_k|^2 + \frac{\sigma_x^2}{N_0}} $$ So you can see ...

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2 answers
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162 views
Minimum value of G (Amplitude) that guarantees an error probability of at least $10^{-2}$ in a 32-PAM transmission system
1 votes

I am not sure if you can use $P_{err}=\text{erfc}(G/\sigma)$ because noise is not gaussian distributed. Here is my take on it. Assuming uniform probability of transmission for all 32 symbols $x_i$,...

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2 answers
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285 views
How to calculate EVM in %age of an Equalized Constellation in 16QAM?
1 votes

From my experience EVM is defined as $$ EVM = \sqrt{\frac{1}{NP_{avg}}\sum_{n=0}^{n=N-1}(|x_n-x^*_n|^2)}\\ EVM_{\%} = EVM \times 100 $$ where $x_n$ is the equalized symbol, and $x^*_n$ is the ...

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3 answers
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148 views
Nyquist Rate of cosine modulated function
1 votes

Update: I feel there is no need to bring concept of Bandpass sampling (as mentioned in comments below) because this is specifically regarding a simple misunderstanding that OP has. The text referenced ...

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70 views
Is DFE equalizer always blind or can we use reference signal?
1 votes

I can answer for adaptive filter containing feedback path alone as I have implemented it recently (both Blind DFE and with Reference Symbols), but it should work for DFE containing feed-forward path ...

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3 answers
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127 views
Simplifying frequency response equation
1 votes

$\begin{align} 1-e^{-j4\omega} &=1-(\cos(4\omega)-j\sin(4\omega))\\ &=1-\cos(4\omega)+j\sin(4\omega)\\ &=1-(1-2\sin^2(2\omega))+j2\sin(2\omega)\cos(2\omega)\\ &=2\sin(2\omega)(\sin(2\...

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374 views
Cross correlation and cross power spectrum for signal + noise
1 votes

$S_{xy}=S_{xx}$ is true but this does not mean $F_x*F_y = F_x*F_x$ when $y$ is random. The actual definition is $$S_{xy}(f)=\lim_{T\rightarrow \infty}\textbf{E}\{F^*_xF_y\}$$ for random signals. ...

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1 answers
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52 views
LowPass Filter & Window *Img & Code* - Frequency Response has no lobe roll off
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1 votes

You need to zero pad the FFT so that it reveals more of the frequency response (increasing the resolution of the plot). I corrected your code (while taking fft, I took 1024 point FFT for windows as ...

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2 answers
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28 views
What does following statement mean: " Simulation was done at the rate of 12 samples per cycle of 50Hz a.c."
1 votes

One cycle duration of 50Hz is 0.02seconds. So this means you need to take 12 samples in a duration of 0.02s. In one second, there will be 600 samples (sample rate of 600 samples per second).

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2 answers
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45 views
Filter Percentage Uniform Noise from a DC-signal?
1 votes

Taking the average values of these measurements should work. The estimator is $$ \hat{X}=\frac{1}{L}\sum_0^{L-1}K=\frac{1}{L}\sum_0^{L-1}(X+X*N) $$ .To show that it is the unbiased estimator, $$ E(\...

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75 views
What is the physical meaning of coherence bandwidth in mmWave massive MIMO channel?
1 votes

In contrast to your previous question(Why multi-path channel has linear phase within the coherence bandwidth?), the coherence BW in mmWave may not be relevant considering delay spread alone. If you ...

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3 answers
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56 views
what are some possible reasons of having duplicates in sensor signal? resulting in stair-step signal?
1 votes

There are multiple possibilities. One, as you said, cellphone may not be capable of 500Hz so it duplicates values. Did you verify whether cellphone is capable of it? Two, gyroscope output itself ...

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6 answers
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638 views
Design a LTI system which returns DC value of the input signal
1 votes

For a finite energy signal (zero power), the time average is zero. For a periodic signal (finite power but infinite energy), MattL has already mentioned that frequency components are present at $f =k/...

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1 answers
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451 views
How to convert my transfer function to the frequency domain
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1 votes

Since this is not an LTI system, we cannot have $H(\omega) = K\Theta_1(\omega)$, where $K$ is a scalar complex number. But as OP mentioned in the comment he has knowledge of $\Theta_1(\omega)$, we can ...

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