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Adding Independent Noise

Signal processing often involves managing and optimizing Signal to Noise Ratio (SNR). To achieve this, one may need to work with noise budgets and ensure that any additional additive noise sources are ...
Dan Boschen's user avatar
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8 votes
2 answers
191 views

What is the frequency response of a filter with impulse response $h(t)=\frac{\cos(\omega_0t)}{\pi t}$?

Most of us have come across the impulse response of an ideal (continuous-time, unity gain) low pass filter with cut-off frequency $\omega_0$: $$h_{LP}(t)=\frac{\sin(\omega_0t)}{\pi t}\tag{1}$$ The ...
Matt L.'s user avatar
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3 votes
3 answers
134 views

Subtract Lowpass from Wire to Get Allpass

One technique to make a high pass filter is to subtract a lowpass filter from a wire (meaning subtract the output of the filter from the input as I have demonstrated in this post). What lowpass can ...
Dan Boschen's user avatar
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2 votes
0 answers
56 views

Effect of Passband Slope on a BPSK Constellation

What is the effect of a passband slope on a BPSK constellation? (This is a companion question to the related "DSP Puzzle" for QPSK) Specifically given a linear slope (in magnitude, not dB), ...
Dan Boschen's user avatar
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5 votes
1 answer
248 views

Effect of Passband Slope on QPSK Constellation

What is the effect of a passband slope on a QPSK (or any QAM) constellation? Specifically given a linear slope (in magnitude, not dB), and no phase distortion (linear phase or even zero-phase) how ...
Dan Boschen's user avatar
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0 votes
1 answer
239 views

Questions about the sampling frequency mapping relation to 2π

Continued from the previous two questions Q3: When $f_o$ isn't a multiple of $F_s$ , can $F_s$ still map to $2\pi$? Answer: $F_s$ always map to $2\pi$ under digital (normalized) frequency domain. Q4:...
Ran's user avatar
  • 19
0 votes
1 answer
144 views

How and why does sample frequency Fs be mapped to 2π?

Q1: Can anyone give a further explanation on this sentence? Each time $f_o$ is a multiple of $F_s$, the argument of the exponential is a multiple of $2\pi$ Q2: - must $f_o$ be a multiple of $F_s$?
Ran's user avatar
  • 19
2 votes
0 answers
154 views

How to demodulate DominoEx-like signal with liquid dsp?

I found a proprietary protocol that is used on ham radio bands. The author have published details,claiming that it's a version of DominoEX with slightly different baud rate and FEC. I want to try to ...
Albert DeVasques's user avatar
3 votes
1 answer
187 views

Algorithm to Count Zeros Outside Unit Circle for FIR Filter

As detailed in this post Can I set a constraint on the first tap of an FIR filter such that its inverse is stable? I show how Cauchy's Argument Principle can be used to easily confirm if an FIR filter ...
Dan Boschen's user avatar
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1 vote
1 answer
291 views

Modelling zero padded OFDM as circular convolution between channel and FFT frame

This is meant to be a puzzle so please preface your answer with spoiler notation by typing the following two characters first ">!"  An often mentioned negative side of the zero padded OFDM is that it ...
Dsp guy sam's user avatar
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7 votes
1 answer
523 views

2nd Order Type 2 PLL for Tracking Frequency Error

This is a "DSP Puzzle", Please preface your answer with spoiler notation by typing the following two characters first ">!" as the intention is for readers to think through what the solution might be ...
Dan Boschen's user avatar
  • 45.9k
1 vote
2 answers
407 views

Z-Transform and DFT

I have $$H(z) = \frac{\left[b_0 + b_1 \cdot z^{-1}\right]}{\left[1 + a_1z^{-1} + a_2 \cdot z^{-2}\right]}$$. Why is it that I can calculate the spectrum between $0$ and $0.5 \cdot f_s$ by calculating ...
dimwit_recluse's user avatar
1 vote
1 answer
107 views

Amplitude modulation in pure sine wave [duplicate]

I am generating sine wave in MATLAB with following code ...
user777304's user avatar
-1 votes
1 answer
2k views

What do the filter coefficients in digital filter represent?

Could you help me? How can I understand the function of the filter coefficients practically? In the simple case, it is the impulse response of the LTI system. but how do they work?
reem's user avatar
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12 votes
9 answers
1k views

Where is the flaw in this derivation of the DTFT of the unit step sequence $u[n]$?

This question is related to this other question of mine where I ask for derivations of the discrete-time Fourier transform (DTFT) of the unit step sequence $u[n]$. During my search for derivations I ...
Matt L.'s user avatar
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7 votes
1 answer
665 views

Simplest All Digital GMSK Modulator

How to simply implement an all digital GMSK modulator with no multipliers? The implementation approach should be applicable to GMSK modulation with $BT=0.5$ or less (where intentional ISI is ...
Dan Boschen's user avatar
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6 votes
3 answers
2k views

More Simultaneous Dynamic Range with Fixed Point or Floating Point?

What data path would have more simultaneous dynamic range: 32 bit fixed-point or 32 bit floating-point? Why? To clarify "simultaneous dynamic range": This is the ability to discern strong ...
Dan Boschen's user avatar
  • 45.9k
7 votes
3 answers
4k views

Nyquist's Stability Criterion and Cauchy's Argument Principle

Background: Nyquist's Stability Criterion for linear-time-invariant systems makes use of Cauchy's argument principle to determine if any zeros in the characteristic equation are in the right-half ...
Dan Boschen's user avatar
  • 45.9k
5 votes
1 answer
372 views

Convert a Park McClellan FIR Solution to Achieve Stop-band Roll-off

Often it is more desirable to have a roll-off versus frequency of the rejection in the stopband; for example resampling filters where all the alias image locations fold into the first Nyquist Zone. ...
Dan Boschen's user avatar
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5 votes
2 answers
2k views

Double the "speed", double the frequency?

Usually, when some sample is played-back at twice the rate it was recorded, the pitch of the recording sounds an octave higher. For example: $g(t) = \sin(2 \pi f t)$ and $g(2t) = \sin(2 \pi f 2 t) \...
A_A's user avatar
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4 votes
1 answer
2k views

How do you simultaneously undersample and oversample?

"Undersampling" and "Oversampling" are common terms when referring to the choice of sampling frequency for analog to digital data conversion. Is it possible to Undersample and Oversample a waveform ...
Dan Boschen's user avatar
  • 45.9k
3 votes
2 answers
1k views

Minimum Output Samples needed to crack a "Gold Code" Generator (Dual LFSR)

Please preface your answer with spoiler notation by typing the following two characters first ">!" Below is an implementation of a "Gold Code" Generator formed by adding (in $GF(2)$) the outputs from ...
Dan Boschen's user avatar
  • 45.9k
15 votes
2 answers
2k views

How to build a phase shifter with arbitrary phase shift

Fred, a DSP engineer, goes to his favorite DSP store to do some shopping. Fred: Hi, I'd like to buy a phase shifter. Shop assistant: Hmm, what exactly do you mean? Fred: Well, you know, if you put ...
Matt L.'s user avatar
  • 85.9k
4 votes
1 answer
1k views

Simulation of a Frequency ramp

This might be an easy one! Please preface your answer with spoiler notation by typing the following two characters first ">!" Given the following equation that describes a cosine wave as a function ...
Dan Boschen's user avatar
  • 45.9k
8 votes
2 answers
1k views

Gaussian FIR filter with no multipliers?

What is the simplest way to implement a Gaussian FIR filter with unity gain coefficients and no multipliers? Please preface your answer with spoiler notation by typing the following two characters ...
Dan Boschen's user avatar
  • 45.9k
3 votes
5 answers
563 views

$9\rm V$ Battery with $45^\circ$ phase

How can you implement a $9\rm V$ battery with a phase of $45^\circ$? (As a black box with a DC Voltage of $9\rm V$ and a phase of $45^\circ$) Please preface your answer with spoiler notation by ...
Dan Boschen's user avatar
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