DSP Archives | Page 8 of 15

December 22, 2017 DSP

Interpreting Time Domain Derivative in Frequency Domain

Although this article explains the concepts in terms of mathematical constants e and j as well as integration, my book on SDR steers clear of the complex notation and integrals to describe the underlying concepts from the ground up to an advanced level. One of the properties of Fourier Transform is that the derivative of a signal in time domain gets translated to multiplication of the signal spectrum by $j2\pi f$ in frequency domain. This property is usually derived as follows. For a signal $s(t)$ with Fourier Transform $S(f)$ \begin{equation*} s(t) = \frac{1}{2\pi}\int \limits _{-\infty}^{+\infty} S(f) e^{j2\pi ft}df, \end{equation*} we

October 24, 2022 DSP

On Analog-to-Digital Converter (ADC), 6 dB SNR Gain per Bit, Oversampling and Undersampling

We have discussed before the sampling on time axis for analog to digital (A/D) conversion. An Analog to Digital Converter (ADC) produces the samples $x[n]$ of a continuous-time signal $x(t)$ at its input. Ideally, these samples are the exact values of the signal $x(t)$ at time instants $nT_s$ where $T_s=1/f_s$ is the sampling period. In practice, however, there are imperfections both on the y-axis and the x-axis. On y-axis, an ADC has a finite resolution depending on the number of bits used for quantization. On x-axis, there are issues of clock jitter that distort the samples produced. In this article,

Number of goals scored by player 1 in each match

May 13, 2019 DSP

Basic Signals

As we saw here, a signal is any measurable quantity that varies with time (or some other independent variable). Classification of continuous-time and discrete-time signals deals with the type of independent variable. If the signal amplitude is defined for every possible value of time, the signal is called a continuous-time signal. However, if the signal takes values at specific instances of time but not anywhere else, it is called a discrete-time signal. Basically, a discrete-time signal is just a sequence of numbers. Example Consider a football (soccer) player participating in a 20-match tournament. Suppose that his running speed is recorded

Bandwidth, power and DSP correspond to the traditional trio of raw materials, energy and knowledge

October 21, 2020 DSP / Wireless/SDR

Why Building an SDR Requires DSP Expertise

In an introduction to signals, we discussed the idea that the any activities around us, starting from subatomic particles to massive societal networks, are generating signals all the time. Since mathematics is the language of the universe and digital signals are nothing but quantized number sequences, it is fair to say that the workings of the universe can be mapped to an infinitely large set of signals. With these number sequences in hand, an electronic computer can process the signals and either extract the information about the surrounding real world phenomena or even better influence its target environment. We saw

Square-root Nyquist filters for three different excess bandwidths

September 16, 2017 DSP / Wireless/SDR

How to Design Nyquist and Square-Root Nyquist Pulse Shaping Filters

The radio spectrum is a very precious resource like real estate and must be utilized judiciously. Pulse shaping filters control the spectral leakage of the transmitted signal in a wireless channel due to the strict restrictions to comply with a spectral mask. This is even more important for the upcoming 5G wireless systems which are based on a variety of wireless transmission protocols (such as mobile networks, Internet of Things (IoT) and machine to machine communications) combined in one comprehensive standard. Even for wired channels, there is always a natural bandwidth of the medium (copper wire, coaxial cable, optical fiber)