Project Report : Digital Filter Blocks in MyHDL and their integration in pyFDA
The Google Summer of Code 2018 is now in its final stages, and I’d like to take a moment to look back at what goals were accomplished, what remains to be completed and what I have learnt. The project overview was discussed in the previous blog...
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
Last time, we talked about error correction and detection, covering some basics like Hamming distance, CRCs, and Hamming codes. If you are new to this topic, I would strongly suggest going back to read that article before this one. This time we...
Digital PLL’s, Part 3 – Phase Lock an NCO to an External Clock
Sometimes you may need to phase-lock a numerically controlled oscillator (NCO) to an external clock that is not related to the system clocks of your ASIC or FPGA. This situation is shown in Figure 1. Assuming your system has an...
Two Easy Ways To Test Multistage CIC Decimation Filters
This article presents two very easy ways to test the performance of multistage cascaded integrator-comb (CIC) decimation filters. Anyone implementing CIC filters should take note of the following proposed CIC filter test methods.
ADC Clock Jitter Model, Part 2 – Random Jitter
In Part 1, I presented a Matlab function to model an ADC with jitter on the sample clock, and applied it to examples with deterministic jitter. Now we’ll investigate an ADC with random clock jitter, by using a filtered or unfiltered...
ADC Clock Jitter Model, Part 1 – Deterministic Jitter
Analog to digital converters (ADC’s) have several imperfections that affect communications signals, including thermal noise, differential nonlinearity, and sample clock jitter [1, 2]. As shown in Figure 1, the ADC has a sample/hold...
FFT Interpolation Based on FFT Samples: A Detective Story With a Surprise Ending
This blog presents several interesting things I recently learned regarding the estimation of a spectral value located at a frequency lying between previously computed FFT spectral samples. My curiosity about this FFT interpolation process was triggered by reading a spectrum analysis paper written by three astronomers.
Phase or Frequency Shifter Using a Hilbert Transformer
In this article, we'll describe how to use a Hilbert transformer to make a phase shifter or frequency shifter. In either case, the input is a real signal and the output is a real signal. We'll use some simple Matlab code to simulate these systems. After that, we'll go into a little more detail on Hilbert transformer theory and design.
An Efficient Linear Interpolation Scheme
This article presents a computationally-efficient linear interpolation trick that requires at most one multiply per output sample.
Simplest Calculation of Half-band Filter Coefficients
Half-band filters are lowpass FIR filters with cut-off frequency of one-quarter of sampling frequency fs and odd symmetry about fs/4 [1]*. And it so happens that almost half of the coefficients are zero. The passband and stopband bandwiths are equal, making these filters useful for decimation-by-2 and interpolation-by-2. Since the zero coefficients make them computationally efficient, these filters are ubiquitous in DSP systems. Here we will compute half-band coefficients using the window method. While the window method typically does not yield the fewest taps for a given performance, it is useful for learning about half-band filters. Efficient equiripple half-band filters can be designed using the Matlab function firhalfband [2].
Polyphase Filters and Filterbanks
ALONG CAME POLY Polyphase filtering is a computationally efficient structure for applying resampling and filtering to a signal. Most digital filters can be applied in a polyphase format, and it is also possible to create efficient resampling...
Music/Audio Signal Processing
Greetings,This is my blog from the point of view of a music/audio DSP research engineer / educator. It is informal and largely nontechnical because nearly everything I have to say about signal processing is (or will be) somewhere in my four-book...
Pulse Shaping in Single-Carrier Communication Systems
Some common conceptual hurdles for beginning communications engineers have to do with "Pulse Shaping" or the closely-related, even synonymous, topics of "matched filtering", "Nyquist filtering", "Nyquist pulse", "pulse filtering", "spectral...
Four Ways to Compute an Inverse FFT Using the Forward FFT Algorithm
If you need to compute inverse fast Fourier transforms (inverse FFTs) but you only have forward FFT software (or forward FFT FPGA cores) available to you, below are four ways to solve your problem. Preliminaries To define what we're...
Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images
This blog explains why, in the process of time-domain interpolation (sample rate increase), zero stuffing a time sequence with zero-valued samples produces an increased-length time sequence whose spectrum contains replications of the original...
An Interesting Fourier Transform - 1/f Noise
Power law functions are common in science and engineering. A surprising property is that the Fourier transform of a power law is also a power law. But this is only the start- there are many interesting features that soon become apparent. This may...
Pentagon Construction Using Complex Numbers
A method for constructing a pentagon using a straight edge and a ruler is deduced from the complex values of the Fifth Roots of Unity. Analytic values for the points are also derived.
Evaluate Window Functions for the Discrete Fourier Transform
The Discrete Fourier Transform (DFT) operates on a finite length time sequence to compute its spectrum. For a continuous signal like a sinewave, you need to capture a segment of the signal in order to perform the DFT. Usually, you...
5G NR QC-LDPC Encoding Algorithm
3GPP 5G has been focused on structured LDPC codes known as quasi-cyclic low-density parity-check (QC-LDPC) codes, which exhibit advantages over other types of LDPC codes with respect to the hardware implementations of encoding and decoding using...
Determination of the transfer function of passive networks with MATLAB Functions
With MATLAB functions, the transfer function of passive networks can be determined relatively easily. The method is explained using the example of a passive low-pass filter of the sixth order, which is shown in FIG.Fig.1 Passive low-pass filter...
