Compute Modulation Error Ratio (MER) for QAM
Neil Robertson shows how to define and compute Modulation Error Ratio (MER) for QAM using a simplified baseband model and decision-slice errors. The post derives per-symbol and averaged MER formulas, explains when MER tracks carrier-to-noise ratio under AWGN and matched root-Nyquist filters, and provides example Pav values for QAM-16 and QAM-64 plus a Matlab script and practical tips.
Plotting Discrete-Time Signals
Neil Robertson demonstrates a practical interpolate-by-8 FIR approach to make sampled signals look like their continuous-time counterparts when plotted. The post explains a 121-tap filter designed for signals up to 0.4*fs, shows Matlab examples for a sinusoid and a filtered pulse, and highlights the transient and design trade-offs so you can reproduce clean plots with the supplied interp_by_8.m code.
Interpolation Basics
Neil Robertson demonstrates interpolation by an integer factor using a frequency-domain approach, showing how zero-insertion followed by an FIR low-pass filter reconstructs a higher-rate signal. The article walks through spectra, passband and stopband selection, and a 41-tap Parks-McClellan filter example applied to a Chebyshev-window test signal. Matlab code and percent-error plots are included so engineers can reproduce and evaluate the method.
Part 11. Using -ve Latency DSP to Cancel Unwanted Delays in Sampled-Data Filters/Controllers
Negative-latency DSP can cancel ADC, FPGA/DSP, DAC and propagation delays to deliver near-zero unwanted latency filtering. Steve Maslen explains how to split a digital filter into a simple feed gain b0 and an advanced DF3 block that produces samples one sample early, then recombine them so sampled-data delays cancel. MATLAB c2d examples, a PID case study and FPGA test-bed results show the technique is practical and proven, with active IP noted.
IIR Bandpass Filters Using Cascaded Biquads
This post provides a Matlab function that builds Butterworth bandpass IIR filters by cascading second-order biquad sections. The biquad approach, implemented in Direct Form II, reduces sensitivity to coefficient quantization, which matters most for narrowband filters. The included biquad_bp function computes each section's feedforward and feedback coefficients plus gains from a lowpass prototype order, center frequency, bandwidth, and sampling rate.
Generating Partially Correlated Random Variables
Designing signals to match a target covariance is simpler than it sounds. This post shows how to build partially correlated complex signals by hand for the two-signal case, then generalizes to N signals using the Cholesky decomposition. Short MATLAB examples demonstrate the two-line implementation and the article highlights numerical caveats when a covariance is only positive semidefinite.
Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT
This post makes a basic DSP principle tangible by computing the DFT over an extended set of bins and plotting the results. It demonstrates that a sampled signal's spectrum repeats every sampling rate, explains the k-to-frequency mapping, and contrasts common bin ranges such as 0..N-1 and -N/2..N/2-1. The write-up also highlights symmetry for real sequences and recommends using the FFT for efficiency.
The Phase Vocoder Transform
Treating the phase vocoder as a continuous transform, this post frames PV(x,α,β) as a bijection on signal space and derives the domain constraints needed for an inverse mapping. It uses geometric intuition and group-theory analogies to explain negative and zero scalings, then brings the idea back to DSP to show how aliasing and phase artifacts appear. The Laroche and Dolson consistency measure D_M plus MATLAB experiments are used to compare classic and identity phase-locking reconstructions.
Compute the Frequency Response of a Multistage Decimator
This post shows a practical way to compute the full frequency response of a multistage decimator by representing every stage at the input sample rate. The author walks through upsampling lower-rate FIR coefficients, convolving to form the overall impulse response, and taking a DFT, then demonstrates how aliasing and stopband placement affect the aliased components. Example Matlab code and plots illustrate each step.
Use Matlab Function pwelch to Find Power Spectral Density -- or Do It Yourself
Neil Robertson walks through using Matlab's pwelch and shows how to implement PSD estimation yourself with fft. The post uses concrete examples and complete m-files to demonstrate window selection, converting pxx (W/Hz) to W/bin, Welch DFT averaging, and a worked C/N0 calculation. Readers get practical, runnable recipes for accurate spectrum units, variance reduction with averaging, and peak-power extraction.
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.
Multi-Decimation Stage Filtering for Sigma Delta ADCs: Design and Optimization
A Matlab toolbox streamlines the design and optimization of multi-stage decimation filters for sigma-delta ADCs. MSD-toolbox automates stage-count and decimation-factor selection, generates Parks-McClellan equiripple FIR coefficients, and iteratively selects coefficient quantization to meet in-band noise constraints. It accepts sigma-delta bitstream stimuli for spectral and intra-stage analysis, includes cost estimation routines, and is published open-source on MathWorks with examples and a dissertation reference.
A Simplified Matlab Function for Power Spectral Density
Neil Robertson provides a tiny Matlab wrapper around pwelch that simplifies PSD computation by preselecting a Kaiser window, default overlap, and converting units from W/Hz to dBW/bin. Call psd_simple(x,nfft,fs) to get PdB and a frequency vector, with nfft controlling whether DFT averaging is used. The post includes examples showing the effect of averaging and explains the Kaiser window processing loss.
Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT
This post makes a basic DSP principle tangible by computing the DFT over an extended set of bins and plotting the results. It demonstrates that a sampled signal's spectrum repeats every sampling rate, explains the k-to-frequency mapping, and contrasts common bin ranges such as 0..N-1 and -N/2..N/2-1. The write-up also highlights symmetry for real sequences and recommends using the FFT for efficiency.
Third-Order Distortion of a Digitally-Modulated Signal
Amplifier third-order distortion is a common limiter in RF and communications chains, and Neil Robertson walks through why it matters using hands-on MATLAB simulations. He shows how a cubic nonlinearity creates IMD3 tones, causes spectral regrowth and degrades QAM constellations, and gives practical notes on estimating k3, computing ACPR from PSDs, and sampling considerations.
Discrete Wavelet Transform Filter Bank Implementation (part 1)
David Valencia walks through a practical implementation of discrete wavelet transform filter banks, focusing on cascading branches and efficient equivalent filters. He contrasts DWT and DFT resolution behavior and shows how cascading the low-pass branch sharpens frequency division while the high-pass path remains unchanged. Code pointers and a preview of formfilters() demonstrate how to compute only the needed samples by combining filters with upsampling.
ADC Clock Jitter Model, Part 1 -- Deterministic Jitter
Clock jitter on ADC sample clocks corrupts high-frequency signals, and this post builds a practical MATLAB model to show exactly how deterministic (periodic) jitter maps into phase modulation and discrete sidebands. The author explains a parabolic-interpolation approach using twice-rate samples, demonstrates examples from single tones to pulses, and matches simulation spectra to closed-form sideband formulas so engineers can predict jitter effects.
Spline interpolation
Markus Nentwig provides a cookbook for segmented cubic spline interpolation that turns scattered or noisy data into efficient fixed-point functions. The article shows how to build third-order polynomial segments with explicit value and slope control via basis functions, solve scaling factors by least-squares in Octave/Matlab, and export coefficients for Verilog RTL evaluation using the Horner scheme and practical fixed-point tips.
Design IIR Highpass Filters
Neil Robertson walks through a compact, six-step procedure to synthesize IIR Butterworth highpass filters using pre-warping and the bilinear transform. The post gives the pole transformations, the placement of N zeros at z=1, the scaling to unity gain at fs/2, and a ready-to-run MATLAB hp_synth implementation that reproduces MATLAB's butter results.
Fitting Filters to Measured Amplitude Response Data Using invfreqz in Matlab
This post is a redirect notice for a code snippet now hosted elsewhere. If you were looking for the invfreqz example on fitting a filter to measured amplitude response data, this page simply points you to the new location and asks you to update your bookmark.
Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT
This post makes a basic DSP principle tangible by computing the DFT over an extended set of bins and plotting the results. It demonstrates that a sampled signal's spectrum repeats every sampling rate, explains the k-to-frequency mapping, and contrasts common bin ranges such as 0..N-1 and -N/2..N/2-1. The write-up also highlights symmetry for real sequences and recommends using the FFT for efficiency.
Part 11. Using -ve Latency DSP to Cancel Unwanted Delays in Sampled-Data Filters/Controllers
Negative-latency DSP can cancel ADC, FPGA/DSP, DAC and propagation delays to deliver near-zero unwanted latency filtering. Steve Maslen explains how to split a digital filter into a simple feed gain b0 and an advanced DF3 block that produces samples one sample early, then recombine them so sampled-data delays cancel. MATLAB c2d examples, a PID case study and FPGA test-bed results show the technique is practical and proven, with active IP noted.
Discrete Wavelet Transform Filter Bank Implementation (part 1)
David Valencia walks through a practical implementation of discrete wavelet transform filter banks, focusing on cascading branches and efficient equivalent filters. He contrasts DWT and DFT resolution behavior and shows how cascading the low-pass branch sharpens frequency division while the high-pass path remains unchanged. Code pointers and a preview of formfilters() demonstrate how to compute only the needed samples by combining filters with upsampling.
Compute Modulation Error Ratio (MER) for QAM
Neil Robertson shows how to define and compute Modulation Error Ratio (MER) for QAM using a simplified baseband model and decision-slice errors. The post derives per-symbol and averaged MER formulas, explains when MER tracks carrier-to-noise ratio under AWGN and matched root-Nyquist filters, and provides example Pav values for QAM-16 and QAM-64 plus a Matlab script and practical tips.
Instantaneous Frequency Measurement
Measuring carrier frequency quickly and with minimal data matters in radar and signal characterization. Parth Vakil explains the delay-and-multiply instantaneous frequency measurement technique, shows how analytic signals and multiple delays resolve the 2π ambiguity, and demonstrates noise, phase-wrapping, and interferer effects using MATLAB code. He also outlines practical mitigations like phase unwrapping and channelization.
Design study: 1:64 interpolating pulse shaping FIR
Markus Nentwig presents a practical 1:64 root-raised cosine interpolator built from cascaded FIR stages that slashes computational cost. By separating pulse shaping from rate conversion, designing each interpolator to suppress only known alias bands, and equalizing the pulse shape, the design achieves just 4.69 MACs per output, roughly 12 percent of a straight polyphase implementation while meeting EVM targets.
ADC Clock Jitter Model, Part 1 -- Deterministic Jitter
Clock jitter on ADC sample clocks corrupts high-frequency signals, and this post builds a practical MATLAB model to show exactly how deterministic (periodic) jitter maps into phase modulation and discrete sidebands. The author explains a parabolic-interpolation approach using twice-rate samples, demonstrates examples from single tones to pulses, and matches simulation spectra to closed-form sideband formulas so engineers can predict jitter effects.
Design IIR Band-Reject Filters
This post walks through designing IIR Butterworth band-reject filters and provides two MATLAB synthesis functions, br_synth1.m and br_synth2.m. br_synth1 accepts a null frequency plus an upper -3 dB frequency, while br_synth2 takes lower and upper -3 dB frequencies. The author demonstrates an example where a 2nd-order prototype yields a 4th-order H(z), prints b and a coefficients, and plots the response using freqz.
A Narrow Bandpass Filter in Octave or Matlab
Building very narrow FIR bandpass filters at high sample rates often yields extremely long impulse responses. This post shows a practical Octave/Matlab implementation that uses complex downconversion to baseband plus a multistage Matrix IFIR and running-sum cascade to slash computation. With the provided example (48 kHz, 850 Hz center, 10 Hz passband) you get <1 dB ripple and >60 dB stopband while running 20x to 100x faster than a single-stage FIR.
ADC Clock Jitter Model, Part 2 – Random Jitter
Neil Robertson shows how to simulate ADC sample-clock random jitter in Matlab, moving from band-limited Gaussian noise to wideband and close-in phase noise. The post highlights practical artifacts such as aliasing of wideband clock noise, the 20*log10 dependence of jitter sidebands on input frequency, and why cubic interpolation plus a custom noise_filter produces accurate rms and spectral results engineers can trust.
