### Dan Boschen (@DanBoschen)

If you want to minimize resources this can be a significant factor and low hanging fruit to get there (there is no need to accumulate 32 bits from each 16x16 multiplier!)....

The concern is when the goal is to optimize resources. It is easy to confirm coefficient scaling through simulation, but quantization noise growth due to truncating...

The multiplier output precision will also be a concern- the quantization noise due to any truncation at the multiplier outputs or the accumulator if truncated multiple...

Yes please post a link to your sample files. It's possible I may have some time tomorrow in which case I would be happy to help you generate an example of what you...

Yes, you can replace z^(-1) blocks with fractional delay filters, but that doesn't fall into the category of "minimal changes", as you found to achieve the accuracy...

In the moving average filter, the notches are at the frequency location in Hz that is the reciprocal of the length of the filter in seconds, independent of the...

Glad that it is helpful.If this is for FMCW radar, this article describes the complex-baseband architecture as another option to get the complex analytic signal...

The structure your proposing wouldn't be feasible with a continuous time input, as you would also need to reconstruct to a continuous time output - and to do it...

The phase of the aliases rotates after each delay prior to the down-samplers, and then again after the up-samplers in each of the recreated Nyquist zones. Due to...

I suspect you are getting aliasing effects between the positive and negative frequencies for a real signal (given the finite time duration: the aliasing is the interaction...

The accumulator(s) in the CIC filter are allowed to overflow once in the time duration of the subtractions in the comb(s), as long as the accumulators properly wrap...

Here's an image of the folded linear phase filter in direct form and transposed form: linear_phase_filters.png

Have you considered transposing folded structure? Take the folded linear phase FIR filter and reverse all direction flows, change the adders to branched and branches...

I have a copy my good friend gave me in college in 1986 that I pull of my work desk shelf every other day it seems, and then my mother's copy she had 20 years prior...

One way to do this is with the Hilbert Transform to get the Analytic Signal which would be just the positive frequencies which are represented by the first half...

The Sigma is the accumulator (for Sigma-Delta DAC) or integrator (for Sigma-Delta ADC as shown below) just prior to decision and feedback. The output of the decision...

They are both the same thing and used interchangeably. I must admit that I use both depending on how I wake up in the morning. My impression is Sigma-Delta is more...

I agree with you that the CIC still has viable applications but don't agree that "single bit is very limited". In particular we are seeing more and more single...

... I use the DFT to synthesize antenna patterns in multi-element arrays for this reason. I love it when disciplines overlap to the same underlying principles!

Thanks yes I can't underline enough how much visualizing phasors and working with complex signals simplifies the intuition for DSP. My courses start with this in...

Nice question Kaz! Is “The frequency response is the Fourier Transform of the Impulse Response” an insufficient intuition for you? Perhaps then more intuition...

In most depictions of the standard forms, the feedback coefficients are negated. This is just convenient convention based on how the transfer function as given maps...

The intuition of converting the symmetric or antisymmetric coefficients to real sinusoidal components is helpful for the large subset of all possible FIR filters...

Ah ok! Good clarification- that makes a lot of sense. So in applications where down-sampling is to be done on a multi-bit signal, perhaps the CIC is still a viable...

Very nice fred!!! I laughed out loud at all the intro slides. Yes CIC very bad with floating point. I believe with fixed point we can overflow once with no consequence...

I don’t think you are necessarily “wrong” in your thought process - it is just a matter of being clear on how the frequency axis is scaled. Each block on its...

The z^{-1} blocks shown represent a one sample delay for the sampling rate of that block. With that view, they are all correct as Mth order CIC decimate by 2 filters. Be...

Krishk- Did the update get to the root of your question or is there still some confusion here? It may help to know that for small angles beta, the sidebands due...

An NCO is equivalent to a fractional divider of the master clock. In general when you divide any frequency tone with phase noise by $N$, the phase noise goes down...

I have seen "DDS" referred to the combination of an NCO with a D/A (meaning providing an analog output) whereas an NCO is providing a digitally generated source....

I updated that post to focus on the phase noise cancellation, bottom lined here:This occurs in down-conversion only and not in up-conversion given the output in...

Did your same post on Stack Exchange not answer your question?https://dsp.stackexchange.com/questions/87286/corr...

Often decimation filtering is done very simply with averaging: a CIC decimation filter is mathematically equivalent to a moving average over D samples followed...

Yes, no disagreement with that. I was trying to provide an explanation how it is the same and yet the same processing gain concepts apply (but apparently I didn't...

This does apply equally in reverse, and you are correct that the operations are symmetric other than the sign on the exponential. Further by convention we scale...

Hi David-The FFT is a narrow band filter, and the quantization noise (up to the limits of the SFDR) is spread evenly across all bins, so you can get a lot more bits...

Sorry for my distraction about bin power spread due to windowing which is my preferred use of processing gain in an FFT. My bigger point was there is no actual change...

A noise density is an easier way I think to view this, as the noise density (in power/Hz specifically NOT power/bin) for spread waveforms (such as quantization...

No the power spectral density will remain constant if the transmitter transmits at a constant power the same waveform (since the PSD is the power spread over frequency). There...

Time varying channels due to Doppler and multipath will be a big limitation. If there are no other temporal variations (such as Doppler from movement or channel...

A resampled FIR is also a very good solution for this case (even decimating to implement the LPF and interpolating after if the higher sampling rate is needed)....

Related but those don’t really fit the bill as they are used to compare two complex magnitudes rather than estimate the complex magnitude. However what I didn’t...

Very nice Rick! I didn't know that, thanks for the additional history and nice work. Until I reread the post, I was going to go forward from this point thinking...

This is the "Alpha Max + Beta Min" algorithm as a high-speed approximation for the magnitude of a complex number (or more generically the square root of the sum...

If the RF Bandwidth is 10 MHz there is no need to sample at or more than 30.72 MHz assuming complex baseband samples —sampling at twice the FFT sampling rate...

This is also referred to as “undersampling”. Key requirements and considerations to do this properly are that the analog input bandwidth of the ADC surpasses...

Yes you are correct and that Matlab and Octave do the expected conjugation. Apparently your signal has been already conjugated which can occur when the spectrum...

What may be missing is the complex conjugate that is required when doing a complex correlation. Correlation is the integration of the complex conjugate product of...

Have you considered windowing prior to the FFT? This will minimize the spectral leakage at the expense of widening the main lobe (frequency selectivity). Given you...

I recommend modeling the baseband equivalent signal which is the complex magnitude and phase versus time (the analytic signal moved to DC). There is no reason to...

Thanks, that is handy! The derivation now that I think about it seems straightforward. What we see is we are just lowering "S" in SNR directly: SNR = 20Log(Sine...

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