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...
The Exponential Nature of the Complex Unit Circle
Introduction This is an article to hopefully give an understanding to Euler's magnificent equation: $$ e^{i\theta} = cos( \theta ) + i \cdot sin( \theta ) $$ This equation is usually proved using the Taylor series expansion for the given...
The Number 9, Not So Magic After All
This blog is not about signal processing. Rather, it discusses an interesting topic in number theory, the magic of the number 9. As such, this blog is for people who are charmed by the behavior and properties of numbers. For decades I've thought...
Signed serial-/parallel multiplication
Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm Summary A detailed discussion of bit-level trickstery in signed-signed multiplication Algorithm based on Wikipedia example Includes a Verilog implementation with...
Understanding and Preventing Overflow (I Had Too Much to Add Last Night)
Happy Thanksgiving! Maybe the memory of eating too much turkey is fresh in your mind. If so, this would be a good time to talk about overflow. In the world of floating-point arithmetic, overflow is possible but not particularly common. You can...
Goertzel Algorithm for a Non-integer Frequency Index
If you've read about the Goertzel algorithm, you know it's typically presented as an efficient way to compute an individual kth bin result of an N-point discrete Fourier transform (DFT). The integer-valued frequency index k is in the range of...
Adventures in Signal Processing with Python
Author’s note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don’t need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being...
Python scipy.signal IIR Filtering: An Example
Introduction In the last posts I reviewed how to use the Python scipy.signal package to design digital infinite impulse response (IIR) filters, specifically, using the iirdesign function (IIR design I and IIR design...
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...
Discrete Wavelet Transform Filter Bank Implementation (part 2)
Following the previous blog entry: http://www.dsprelated.com/showarticle/115.php Difference between DWT and DWPT Before getting to the equivalent filter obtention, I first want to talk about the difference between DWT(Discrete Wavelet...
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...
Off Topic: The True Gravitational Geodesic
The third of my off topic Physics series resulting in the true gravitational geodesic equation and some surprising results about gravity.
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...
An Efficient Full-Band Sliding DFT Spectrum Analyzer
In this blog I present two computationally efficient full-band discrete Fourier transform (DFT) networks that compute the 0th bin and all the positive-frequency bin outputs for an N-point DFT in real-time on a sample-by-sample basis. An Even-N...
Exponential Smoothing with a Wrinkle
Introduction This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by providing a set of preprocessing filters to improve the resolution of the DFT. Because of the exponential nature of...
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].
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...
