DSP Related Blogs
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DSP Related Blogs
1M ago
Sigma-delta digital-to-analog converters (SD DAC’s) are often used for discrete-time signals with sample rate much higher than their bandwidth. For the simplest case, the DAC output is a single bit, so the only interface hardware required is a standard digital output buffer. Because of the high sample rate relative to signal bandwidth, a very simple DAC reconstruction filter ..read more
DSP Related Blogs
3M ago
As the name indicates, a digital to analog converter (DAC) converts a digital quantity to an analog voltage or current. But more than this, a DAC converts a discrete-time signal into a continuous-time signal. The latter operation is almost always accomplished by a zero-order hold (ZOH) function. As we’ll see, it is the ZOH that causes the sinx/x roll-off in the frequency ..read more
DSP Related Blogs
5M ago
In my last post, I provided coefficients for several multiplierless half-band FIR filters [1]. In the comment section, Rick Lyons mentioned that such filters would be useful in a multi-stage decimator, as shown in Figure 1 for the decimate-by-8 case. For such an arrangement, any subsequent multipliers save on resources, since they operate at 1/8th of the maximum sample frequency or ..read more
DSP Related Blogs
5M ago
Introduction
This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by deriving frequency formula for the closely related Discrete Time Fourier Transform (DTFT). The distinction between the two is the latter has a domain on the integers from negative infinity to positive infinity and can be evaluated for any frequency. The DFT has a finite ..read more
DSP Related Blogs
6M ago
Introduction
This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by showcasing a special case of the Roots of Unity, which underly the DFT. Admittedly, five bin DFTs aren't used too often, so in actuality you can consider this article another exercise of using complex numbers in context. The complex plane and the corresponding Cartesian ..read more
DSP Related Blogs
6M ago
This article provides coefficients of multiplierless Finite Impulse Response 7-tap, 11-tap, and 15-tap half-band filters and Hilbert Transformers. Since Hilbert transformer coefficients are simply related to half-band coefficients, multiplierless Hilbert transformers are easily derived from multiplierless half-bands. Image attenuation of the Hilbert transformers presented here is ..read more
DSP Related Blogs
7M ago
Recently, for entertainment, I tried to solve a puzzling algebra problem featured on YouTube [1]. In due course I learned that algebra’s $$(a^x)^y=a^{xy}\qquad\qquad\qquad\qquad\qquad(1)$$
Law of Powers identity is not always valid (not always true) if variable a is real and exponents x and y are complex-valued.
The fact that Eq. (1) can’t reliably be used with complex x and y ..read more
DSP Related Blogs
7M ago
In case you forget or didn't already know, registering for the 2023 DSP Online Conference automatically gives you 10 months of unlimited access to all sessions from previous editions of the conference. So for the price of an engineering book, you not only get access to the upcoming 2023 DSP Online Conference but also to hours upon hours of on-demand DSP gold from some of the best ..read more
DSP Related Blogs
10M ago
Designing an interpolator needn’t be confusing. In this article, I’ll present a simple approach for designing interpolators that takes the guesswork out of determining the stopbands (For a basic introduction to interpolators, see my earlier post [1]).
Figure 1a shows a block diagram of an interpolator, which consists of an up-sampler that increases the sample rate of the input ..read more
DSP Related Blogs
10M ago
This blog presents a most computationally-efficient guaranteed-stable real-time sliding discrete Fourier transform (SDFT) algorithm. The phrase “real-time” means the network computes one spectral output sample, equal to a single-bin output of an N‑point discrete Fourier transform (DFT), for each input signal sample.
Proposed Guaranteed Stable SDFT
My proposed guaranteed stable ..read more