Tag: Frequency Recovery

Signal frequency and analysis frequency are not the same, resulting in DFT leakage and spectrum sampling away from the peak. The spectrum shown here is oversampled by 3 through 3x zero-padded FFT
DSP

Peak Interpolation for Sub-Bin Accuracy in Radar and Communications

In signal processing applications, one frequently encounters the problem of estimating the frequency of a complex sinusoid embedded in noise. For example, a DSP engineer will encounter this problem in the delayed echo of an FMCW radar that directly translates into target range, or in carrier frequency estimation of a wireless communication system after timing synchronization has already been achieved (see Chapter 6 for details of how modulation removal exposes the underlying complex sinusoid). Beyond communications and radar, this frequency estimation is also heavily relied upon in digital pitch tracking, speech synthesis, active and passive sonar detection, Doppler ultrasound and

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Classification of carrier frequency synchronization algorithms
Wireless and SDR

Classification of Carrier Frequency Synchronization Techniques

We have discussed before that carrier phase synchronization is done at the end of the Rx signal processing chain due to the very nature of the DSP implementation. And that almost all DSP based phase synchronization algorithms are timing-aided. Timing acquisition implies knowing the symbol boundaries in the Rx sampled waveform which is equivalent to identifying the optimal sampling instants where the eye opening is maximum and Inter-Symbol Interference (ISI) from the neighbouring symbols is zero. In the case of Carrier Frequency Synchronization (CFO), this is not true. From a previous post on the effect of CFO, we know that

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Three different cases for carrier frequency offset
Wireless and SDR

What is Carrier Frequency Offset (CFO) and How It Distorts the Rx Symbols

In Physics, frequency in units of Hz is defined as the number of cycles per unit time. Angular frequency is the rate of change of phase of a sinusoidal waveform with units of radians/second. \begin{equation*} 2\pi f = \frac{\Delta \theta}{\Delta t} \end{equation*} where $\Delta\theta$ and $\Delta t$ are the changes in phase and time, respectively. A Carrier Frequency Offset (CFO) usually arises due to two reasons. The video below also explains this concept. [Frequency mismatch between the Tx and Rx oscillators] No two devices are the same and there is always some difference between the manufacturer’s nominal specification and the

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A discrete-time PLL with a PI loop filter and an NCO consisting of a phase accumulator and a Look-Up Table (LUT)
Wireless and SDR

Phase Locked Loop (PLL) in a Software Defined Radio (SDR)

IBM Watson and Google DeepMind are the most complex computers that, some believe, will try to run the world in a distant future. A PLL on the other hand is the simplest computer that actually runs so much of the world as a fundamental component of intelligent electronic circuits. The PLL was invented by the French engineer Henri de Bellescize in 1932 when he published his first implementation in the French journal L’Onde Electrique. A Phase Locked Loop (PLL) is a device used to synchronize a periodic waveform with a reference periodic waveform. In essence, it is an automatic control

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Known training sequence (a preamble) is prepended, or training can also be inserted periodically within the message
Wireless and SDR

Basics of Synchronization

In every digital communication system, the Tx has the easier role of signal generation while the Rx has the tougher job of figuring out the intended message. Just like solving a puzzle told by someone. Estimating and compensating for the frequency, phase and timing offsets between Tx and Rx oscillators is one such challenge. The solution can be designed depending on many factors such as some part of data is known (called a ‘training sequence’) or not, the synchronizer needs to be one-shot or continuously updating, and so on. Known Data Availability Depending on the availability of known data, synchronization

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