Compute Images/Aliases of CIC Interpolators/Decimators
Cascade-Integrator-Comb (CIC) filters are efficient fixed-point interpolators or decimators. For these filters, all coefficients are equal to 1, and there are no multipliers. They are typically used when a large change in sample...
Four Ways to Compute an Inverse FFT Using the Forward FFT Algorithm
If you need to compute inverse fast Fourier transforms (inverse FFTs) but you only have forward FFT software (or forward FFT FPGA cores) available to you, below are four ways to solve your problem. Preliminaries To define what we're...
Implementing Impractical Digital Filters
This blog discusses a problematic situation that can arise when we try to implement certain digital filters. Occasionally in the literature of DSP we encounter impractical digital IIR filter block diagrams, and by impractical I mean block...
Wavelets I - From Filter Banks to the Dilation Equation
This is the first in what I hope will be a series of posts about wavelets, particularly about the Fast Wavelet Transform (FWT). The FWT is extremely useful in practice and also very interesting from a theoretical point of view. Of course there...
An Efficient Linear Interpolation Scheme
This article presents a computationally-efficient linear interpolation trick that requires at most one multiply per output sample.
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.
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...
Should DSP Undergraduate Students Study Z-transform Regions of Convergence?
Not long ago I presented my 3-day DSP class to a group of engineers at Tektronix Inc. in Beaverton Oregon [1]. After I finished covering my material on IIR filters' z-plane pole locations and filter stability, one of the Tektronix engineers asked...
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...
A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT
Introduction This is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by deriving an exact formula for the frequency of a complex tone in a DFT. It is basically a parallel treatment to the real case...
A New Contender in the Quadrature Oscillator Race
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...
Learn to Use the Discrete Fourier Transform
Discrete-time sequences arise in many ways: a sequence could be a signal captured by an analog-to-digital converter; a series of measurements; a signal generated by a digital modulator; or simply the coefficients of a digital filter. We may wish to know the frequency spectrum of any of these sequences. The most-used tool to accomplish this is the Discrete Fourier Transform (DFT), which computes the discrete frequency spectrum of a discrete-time sequence. The DFT is easily calculated using software, but applying it successfully can be challenging. This article provides Matlab examples of some techniques you can use to obtain useful DFT’s.
Somewhat Off Topic: Deciphering Transistor Terminology
I recently learned something mildly interesting about transistors, so I thought I'd share my new knowledge with you folks. Figure 1 shows a p-n-p transistor comprising a small block of n-type semiconductor sandwiched between two blocks of p-type...
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...
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 Fast Real-Time Trapezoidal Rule Integrator
This article presents a computationally-efficient network for computing real?time discrete integration using the Trapezoidal Rule.
Implementing Impractical Digital Filters
This blog discusses a problematic situation that can arise when we try to implement certain digital filters. Occasionally in the literature of DSP we encounter impractical digital IIR filter block diagrams, and by impractical I mean block...
Music/Audio Signal Processing
Greetings,This is my blog from the point of view of a music/audio DSP research engineer / educator. It is informal and largely nontechnical because nearly everything I have to say about signal processing is (or will be) somewhere in my four-book...
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...
Find Aliased ADC or DAC Harmonics (with animation)
When a sinewave is applied to a data converter (ADC or DAC), device nonlinearities produce harmonics. If a harmonic frequency is greater than the Nyquist frequency, the harmonic appears as an alias. In this case, it is not at once...
The Discrete Fourier Transform of Symmetric Sequences
Symmetric sequences arise often in digital signal processing. Examples include symmetric pulses, window functions, and the coefficients of most finite-impulse response (FIR) filters, not to mention the cosine function. Examining symmetric sequences can give us some insights into the Discrete Fourier Transform (DFT). An even-symmetric sequence is centered at n = 0 and xeven(n) = xeven(-n). The DFT of xeven(n) is real. Most often, signals we encounter start at n = 0, so they are not strictly speaking even-symmetric. We’ll look at the relationship between the DFT’s of such sequences and those of true even-symmetric sequences.
