Digital PLL’s, Part 3 – Phase Lock an NCO to an External Clock

Neil Robertson

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

Rick Lyons

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

Neil Robertson

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...

FFT Interpolation Based on FFT Samples: A Detective Story With a Surprise Ending

Rick Lyons

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

Neil Robertson

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

Rick Lyons

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

Neil Robertson

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].

How to Find a Fast Floating-Point atan2 Approximation

Nic Taylor

Context Over a short period of time, I came across nearly identical approximations of the two parameter arctangent function, atan2, developed by different companies, in different countries, and even in different decades. Fascinated...

A Beginner's Guide to OFDM

Qasim Chaudhari

In the recent past, high data rate wireless communications is often considered synonymous to an Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is a special case of multi-carrier communication as opposed to a conventional...

Sinusoidal Frequency Estimation Based on Time-Domain Samples

Rick Lyons

The topic of estimating a noise-free real or complex sinusoid's frequency, based on fast Fourier transform (FFT) samples, has been presented in recent blogs here on For completeness, it's worth knowing that simple frequency estimation algorithms exist that do not require FFTs to be performed . Below I present three frequency estimation algorithms that use time-domain samples, and illustrate a very important principle regarding so called "exact" mathematically-derived DSP algorithms.