There have been times when I wanted to determine the z-domain transfer function of some discrete network, but my algebra skills failed me. Some time ago I learned Mason's Rule, which helped me solve my problems. If you're willing to learn the...
Filtering Noise: The Basics (Part 1)
IntroductionFinding signals in the presence of noise is one of the fundamental quests of the discipline of signal processing. Noise is inherently random by nature, so a probability oriented approach is needed to develop a mathematical framework...
Evaluate Noise Performance of Discrete-Time Differentiators
When it comes to noise, all differentiators are not created equal. Figure 1 shows the magnitude response of two differentiators. They both have a useful bandwidth of a little less than π/8 radians (based on maximum magnitude response...
Off-Topic: A Fluidic Model of the Universe
Introduction This article is a followup to my previous article "Off Topic: Refraction in a Varying Medium"[1]. Many of the concepts should be quite familiar and of interest to the readership of this site. In the "Speculations" section of my...
Learn About Transmission Lines Using a Discrete-Time Model
We don’t often think about signal transmission lines, but we use them every day. Familiar examples are coaxial cable, Ethernet cable, and Universal Serial Bus (USB). Like it or not, high-speed clock and signal traces on...
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...
A DSP Quiz Question
Here's a DSP Quiz Question that I hope you find mildly interestingBACKGROUNDDue to the periodic natures an N-point discrete Fourier transform (DFT) sequence and that sequence’s inverse DFT, it is occasionally reasonable to graphically plot...
The Discrete Fourier Transform and the Need for Window Functions
The Discrete Fourier Transform (DFT) is used to find the frequency spectrum of a discrete-time signal. A computationally efficient version called the Fast Fourier Transform (FFT) is normally used to calculate the DFT. But, as many...
Modeling Anti-Alias Filters
Digitizing a signal using an Analog to Digital Converter (ADC) usually requires an anti-alias filter, as shown in Figure 1a. In this post, we’ll develop models of lowpass Butterworth and Chebyshev anti-alias filters, and compute the time...
Simulink-Simulation of SSB demodulation
Simulink-Simulation of SSB demodulation or modulation from the article “Understanding the ‘Phasing Method’ of Single Sideband Demodulation” by Richard Lyons Josef Hoffmann The article “Understanding the ‘Phasing Method’ of Single...
A Beginner's Guide To Cascaded Integrator-Comb (CIC) Filters
This article discusses the behavior, mathematics, and implementation of cascaded integrator-comb filters.
There have been times when I wanted to determine the z-domain transfer function of some discrete network, but my algebra skills failed me. Some time ago I learned Mason's Rule, which helped me solve my problems. If you're willing to learn the...
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.
Filtering Noise: The Basics (Part 1)
IntroductionFinding signals in the presence of noise is one of the fundamental quests of the discipline of signal processing. Noise is inherently random by nature, so a probability oriented approach is needed to develop a mathematical framework...
A Fixed-Point Introduction by Example
Introduction The finite-word representation of fractional numbers is known as fixed-point. Fixed-point is an interpretation of a 2's compliment number usually signed but not limited to sign representation. It...
Minimum Shift Keying (MSK) - A Tutorial
Minimum Shift Keying (MSK) is one of the most spectrally efficient modulation schemes available. Due to its constant envelope, it is resilient to non-linear distortion and was therefore chosen as the modulation technique for the GSM cell phone...
Understanding and Relating Eb/No, SNR, and other Power Efficiency Metrics
Introduction Evaluating the performance of communication systems, and wireless systems in particular, usually involves quantifying some performance metric as a function of Signal-to-Noise-Ratio (SNR) or some similar measurement. Many systems...
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...
The Power Spectrum
Often, when calculating the spectrum of a sampled signal, we are interested in relative powers, and we don't care about the absolute accuracy of the y axis. However, when the sampled signal represents an analog signal, we sometimes need an accurate picture of the analog signal's power in the frequency domain. This post shows how to calculate an accurate power spectrum.
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...
