## Third-Order Distortion of a Digitally-Modulated Signal

Analog designers are always harping about amplifier third-order distortion. Why? In this article, we'll look at why third-order distortion is important, and simulate a QAM signal with third order distortion.

## A Narrow Bandpass Filter in Octave or Matlab

The design of a very narrow bandpass FIR filter, coded in either Octave or Matlab, can prove challenging if a computationally-efficient filter is required. This is especially true if the sampling rate is high relative to the filter's center...

## IIR Bandpass Filters Using Cascaded Biquads

In an earlier post [1], we implemented lowpass IIR filters using a cascade of second-order IIR filters, or biquads. This post provides a Matlab function to do the same for Butterworth bandpass IIR filters. Compared to conventional implementations, bandpass filters based on biquads are less sensitive to coefficient quantization [2]. This becomes important when designing narrowband filters.

## Second Order Discrete-Time System Demonstration

Discrete-time systems are remarkable: the time response can be computed from mere difference equations, and the coefficients ai, bi of these equations are also the coefficients of H(z). Here, I try to illustrate this remarkableness by converting a continuous-time second-order system to an approximately equivalent discrete-time system. With a discrete-time model, we can then easily compute the time response to any input. But note that the goal here is as much to understand the discrete-time model as it is to find the response.

## A Beginner's Guide To Cascaded Integrator-Comb (CIC) Filters

This article discusses the behavior, mathematics, and implementation of cascaded integrator-comb filters.

## The correct answer to the quiz of @apolin

The correct answer to the @apolin quiz can be easily explained using the following Simulink model: In MATLAB you have to initialize the two filters: h = dftmtx (8); h1 = h (3, :); % The filter of the quiz h2 = h (7, :); % The...

## A Free DSP Laboratory

Getting Started In Audio DSPImagine you're starting out studying DSP and your particular interest is audio. Wouldn't it be nice to have access to some audio signals and the tools to analyze and modify them? In the old days, a laboratory like this...

## Polynomial calculations on an FIR filter engine, part 1

Polynomial evaluation is structurally akin to FIR filtering and fits dedicated filtering engines quite well, with certain caveats. It’s a technique that has wide applicability. This two-part note discusses transducer and amplifier non-linearity...

## Plotting Discrete-Time Signals

A discrete-time sinusoid can have frequency up to just shy of half the sample frequency. But if you try to plot the sinusoid, the result is not always recognizable. For example, if you plot a 9 Hz sinusoid sampled at 100 Hz, you get the result shown in the top of Figure 1, which looks like a sine. But if you plot a 35 Hz sinusoid sampled at 100 Hz, you get the bottom graph, which does not look like a sine when you connect the dots. We typically want the plot of a sampled sinusoid to resemble its continuous-time version. To achieve this, we need to interpolate.

## 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...

## 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...

## Third-Order Distortion of a Digitally-Modulated Signal

Analog designers are always harping about amplifier third-order distortion. Why? In this article, we'll look at why third-order distortion is important, and simulate a QAM signal with third order distortion.

## 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.

## Frequency Dependence in Free Space Propagation

IntroductionIt seems to be fairly common knowledge, even among practicing professionals, that the efficiency of propagation of wireless signals is frequency dependent. Generally it is believed that lower frequencies are desirable since pathloss...

## Decimators Using Cascaded Multiplierless Half-band Filters

In my last post, I provided coefficients for several multiplierless half-band FIR filters. In the comment section, Rick Lyons mentioned that such filters would be useful in a multi-stage decimator. For such an application, any subsequent multipliers save on resources, since they operate at a fraction of the maximum sample frequency. We’ll examine the frequency response and aliasing of a multiplierless decimate-by-8 cascade in this article, and we’ll also discuss an interpolator cascade using the same half-band filters.

## Setting Carrier to Noise Ratio in Simulations

When simulating digital receivers, we often want to check performance with added Gaussian noise. In this article, I’ll derive the simple equations for the rms noise level needed to produce a desired carrier to noise ratio (CNR or...

## Update to a Narrow Bandpass Filter in Octave or Matlab

Following my earlier blog post (June 2020) featuring a Narrow Bandpass Filter, I’ve had some useful feedback and suggestions. This has inspired me to come up with an updated version, incorporating the following changes compared to the earlier...

## Stereophonic Amplitude-Panning: A Derivation of the "Tangent Law"

This article presents a derivation of the "Tangent Law"

## Frequency Translation by Way of Lowpass FIR Filtering

Some weeks ago a question appeared on the dsp.related Forum regarding the notion of translating a signal down in frequency and lowpass filtering in a single operation [1]. It is possible to implement such a process by embedding a discrete cosine...

## An Astounding Digital Filter Design Application

I've recently encountered a digital filter design application that astonished me with its design flexibility, capability, and ease of use. The software is called the " ASN Filter Designer." After experimenting with a demo version of...