# The Hilbert Transform - Part 2

This is part two of a multi-part series that defines The Hilbert Transform and its significance. In this part we talk about some of the properties of Hilbert Transform.

This is part two of a multi-part series that defines The Hilbert Transform and its significance. In this part we talk about some of the properties of Hilbert Transform.

This is part one of a multi-part series that defines The Hilbert Transform and its significance. 1. Definition The Hilbert transform of a signal is defined as \begin{eqnarray} \mathscr{H}[g(t)] = g(t) * \frac{1}{\pi t} = \frac{1}{\pi} \int_{-\infty}^{\infty} \frac{g(\tau)}{t-\tau} d\tau = \frac{1}{\pi} \int_{-\infty}^{\infty} \frac{g(t-\tau)}{\tau} d\tau \end{eqnarray} The Hilbert transform of is the convolution of with the signal […]

In this post we introduce some great free Electrical Engineering books. Although free sometime means low-quality, but as you will find the books in this list are written buy some of the most well known experts in their fields.

This is the last part of our three-part series that explains the meaning of in digital communication context. Calculating Having understood how Gaussian noise comes to affect transmitted symbols, it remains to define an appropriate average signal energy, and hence a signal-to-noise ratio (SNR). A commonly used definition of SNR is , where is the […]

This is the second part of our three-part series that explains the meaning of in digital communication context. Signal Constellations Often, particularly in the specification of signal sets used in modems, we rely on the notion of an orthonormal basis. A set is an orthonormal basis if The linear span of consists of the […]

This is part one of a three-part series that explains the meaning of in digital communication context. Introduction Every student of communications knows that digital communication system performance—for example, bit error rate (BER) or frame error rate (FER)—depends on the signal-to-noise ratio (SNR), with higher SNRs leading to lower BERs and FERs. Sometimes less clear, […]

Introduction Transmission line theory has been around for more than a century. However, the distributed nature of it has kept it interesting for all these years. One interesting subject is the step response in a hybrid lumped-distributed network. While for a purely lumped network it is quite easy to analyze and derive the response equation, for a distributed or a […]

Oscillators are integral parts of many electronic devices. Majority of fundamental signal processing operations such as frequency translation, synchronization, and timing, require stable clocks derived from an electrical oscillator. An oscillator is generally susceptible to any external periodic signal whose frequency is close to the oscillation frequency or its integer harmonics. Without the loss of […]

In digital communication systems, Analog-to-Digital Converter (ADC) is the main interface between the analog domain and the digital domain. The continuous rising demand for high data rate communication systems has been creating the need for wide-band ADCs with a high sampling rate and high accuracy. These ADCs need to achieve high speed and high resolution […]

This is the second part of our "MATLAB tips and tricks" series. As we also mentioned in part 1, MATLAB is the programming language of choice for many engineers, scientists, data analysts, and more. In this post we introduce some interesting MATLAB tips and tricks. They can be used to make writing code easier and shorter, also to write codes that run faster.