Questions tagged [dsp-puzzle]
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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 ...
- 51.3k
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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 ...
- 51.3k
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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 ...
- 90k
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$9\rm V$ 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 ...
- 51.3k
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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 ...
- 90k
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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 ...
- 51.3k
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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 ...
- 51.3k
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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 ...
- 51.3k
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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 ...
- 51.3k
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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 ...
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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 ...
- 90k
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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 ...
- 51.3k
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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. ...
- 51.3k
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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 ...
- 51.3k
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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 ...
- 51.3k
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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 ...
- 51.3k
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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 ...
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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:...
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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 $F_s$?
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