Frequency – RAYmaps

December 22, 2022December 9, 2024Fundamentals

Demystifying the Fourier Transform

The Fourier Transform is often used in Communication and Signal Processing to find the spectral content of a time-domain signal. The most common example is that of a sinusoid in the time domain, resulting in a sharply peaked signal in the frequency domain, also known as a delta function. A rectangular pulse in the time domain has a more complicated frequency domain equivalent, a sinc function. A rectangular pulse may be thought of as a combination of many sinusoids, hence its frequency domain equivalent is not that straightforward.

March 9, 2022December 9, 20245G, Capacity, Fundamentals

5G Rollout in the USA: Long Way to Go

There is a 3 way race for 5G leadership in the US between T-Mobile(+Sprint), Verizon and AT&T. There are competing claims for the number of 5G subscribers, coverage area and download speeds. But let us look where the 5G industry stands today compared to the expectations a few years back. More than 80% of US population lives in urban areas which comprise of 2% of the total land area of about 10 million squared kilometers. That is 80% of the population lives in an area of about 200,000 squared kilometers.

August 28, 2020June 3, 2022Fundamentals

Phase Lock Loop – Explained

Phase Lock Loops (PLLs) are an important component of communication systems, where they are used for carrier phase and frequency synchronization. They are also used in test and measurement equipment such as in Signal Generators and Vector Network Analyzers (VNAs) for frequency synthesis.

July 27, 2020June 3, 2022Fundamentals

KAY’s Single Frequency Estimator

The basic concept of Kay’s estimator is quite simple. It finds the phase advanced from one sample to the next and this gives us the frequency. Averaging is performed over the time window to get more accurate results. Averaging can be performed using uniform weighting or a weighting function defined by Kay in [1].

July 3, 2020December 9, 2024Fundamentals

A Comparison of FFT, MUSIC and ESPRIT Methods of Frequency Estimation

As discussed in previous posts it is frequently required in communications and signal processing to estimate the frequency of a signal embedded in noise and interference. The problem becomes more complicated when the number of observations (samples) is quite limited. Typically, the resolution in the frequency domain is inversely proportional to the window size in the time domain.

June 17, 2020June 3, 2022Fundamentals

Frequency Estimation Using Zero Crossing Method

In this post we present the simplest method of frequency estimation that is called the Zero Crossing (ZC) method. Since a sine wave crosses the x-axis twice during each cycle, we can simply count the number of crossings and divide it by two and again divide it by the observation window size, giving us the frequency in Hertz.

June 1, 2020June 3, 2022BER Performance

Modeling Phase and Frequency Synchronization Error

Carrier phase or frequency synchronization is a common problem in wireless communication systems. These two problems are interrelated as instantaneous frequency is just the rate of change of phase.

October 28, 2011November 17, 2011LTE

LTE Resource Allocation in Time-Frequency Plane

The LTE standard defines a resource allocation structure in time and frequency domains. If the spatial domain is also considered the resource allocation structure actually becomes a 3-dimensional arrangment. We will ignore the spatial domain for now and focus on the time-frequency plane. In the time domain the LTE transmissions are organized into frames of 10 msec length. Each frame is composed of 10 subframes of 1 msec duration. Each subframe is made up of two equal sized slots of 0.5 msec each. Each slot is composed of 7 or 6 OFDM symbols depending upon whether a short or long […]