Articles | Page 4 of 34

Discrete Fourier Transform (DFT) of a DFT-even sequence

July 11, 2022 DSP

The Beauty of Symmetry in Fourier Transform

In 1978, Fred Harris was a relatively unknown faculty member at the San Diego State University when he published his landmark paper titled On the use of windows for harmonic analysis with the discrete Fourier transform. That paper made him a superstar in DSP community. It presented a brief overview of signal windows and their impact on the detection of harmonic signals in the presence of broad-band noise and nearby harmonic interference. More importantly, he pointed out several common errors in the application of windows when used in the context of Discrete Fourier Transform (DFT). Today I am going to

Computation of the metric involves a correlation sum at a time difference of half symbol duration

June 13, 2022 Wireless/SDR

Timing Synchronization in OFDM Systems

Orthogonal Frequency Division Multiplexing (OFDM) has been the vehicle driving most high rate wireless communication systems in the world today. Some of the notable examples are our WiFi, 4G and 5G technologies. See the interesting LoRa PHY for modulation techniques based on frequency shift – chirp spread spectrum that utilize many of the concepts from OFDM for algorithm design. As a background, we have also discussed before the impact of a timing error on an OFDM signal. It was observed that an integer timing offset does have affect the performance as long as it within certain boundaries. A fractional timing

September 26, 2022 Wireless/SDR

On TeraHertz (THz) Band for Wireless Communication

Larger bandwidth has been the single most contributing factor in higher data rates throughout the history of wireless communication. In the past decade, this resulted in expansion towards mmWave bands that were adopted in 5G systems. Now the trend is continuing towards Tera Hz (THz) bands where large swathes of bandwidth are available for instantaneous and seamless transfer of huge amounts of information. This is because symbol rate $R_M$ is directly proportional to the bandwidth in digitally modulated signals. \[ R_M=\frac{1}{T_M} \propto B \] This is shown in the figure below where a high data rate implies a short symbol

June 6, 2022 Machine Learning

An Intuitive Guide to Linear Regression

We have described before how supervised learning can help us predict a continuous-valued output or organize the input into discrete categories, commonly known as regression and classification problems, respectively. In this article, we describe linear regression and leave the classification algorithms for a future post. What is Linear Regression? Suppose that you are a young investor living in a region with cold climate. One day an idea flashes in your mind that perhaps the shares in the regional stock market climb linearly with the temperature: the better the weather, the higher the prices. You already know what the temperature is

$A comparison of the input to a symbol-spaced versus fractionally-spaced equalizer$

May 2, 2022 Wireless/SDR

A Classification of Equalization Techniques

We have seen before how a wireless channel distorts the Rx signal. The main task of DSP/comms engineer is to remove the Inter-Symbol Interference (ISI) from the Rx samples and recover the correct symbols. Equalization refers to any signal processing technique that eliminates or reduces this ISI before symbol detection. The output of an equalizer should be a Nyquist pulse for a single symbol case from which digital data can be recovered. A conceptual block diagram of such a process is shown below. The equalizer performs the bulk of the signal processing operations required at the Rx for proper demodulation.