A comparison of the input to a symbol-spaced versus fractionally-spaced equalizer
Wireless and 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.

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Synchronization circuit for a Minimum Shift Keying (MSK) modem
Wireless and SDR

Carrier and Clock Synchronization in MSK Signals

Minimum Shift Keying (MSK) is a versatile and spectrally efficient digital modulation scheme. On this website, I have previously written a tutorial on MSK in some detail. We saw how MSK is a special case of Continuous-Phase Frequency Shift Keying (CPFSK) which is a special case of Continuous-Phase Modulation (CPM). We also explored how it can also be cast as Offset Quadrature Phase Shift Keying (OQPSK). In designing a real communication system, the design of modulators and demodulators is the easy part. The main difficulty arises from acquiring synchronization with the incoming signal. Today we investigate the carrier and timing

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Individual and cascade frequency responses as well as group delays of the IIR and all-pass filters combination
DSP

FIR vs IIR Filters – A Practical Comparison

When it comes to practical applications, digital filter design is one of the most important topics in digital signal processing. Today we discuss a critical question encountered in filter design: how to compare the Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filters. Since there is no clear winner, answering this question enables a designer to choose the right solution for their product. A brief comparison of FIR vs IIR filters is now explained below. Computational Complexity It is well known that most practical signals are simply sums of sinusoids. This implies that signals with sharp transition in time

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Multiple paths arriving at the Rx with different strengths and delays
Radar and Localization

Carrier Phase-Based Ranging in Indoor Multipath Channels

Indoor positioning is one of the core technologies behind the idea of Internet of Things (IoT). Some of the use cases are asset tracking and management, factory automation systems, virtual and augmented reality applications, social media relevance and precision marketing in shopping malls. Distances between wireless devices can be determined through various ranging techniques that were introduced in the big picture of localization. Among the candidates, phase based ranging is a low-cost and accurate method that can be implemented on cheap hardware and deployed in real scenarios with relative ease (even in the absence of synchronization among nodes). In this

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Monty Hall at his show Let's Make a Deal
Miscellaneous

The Reason Why the Monty Hall Problem Continues to Perplex Everyone

The Monty Hall problem is an interesting puzzle loosely based on an American TV game show Let’s Make a Deal hosted by Monty Hall. While the puzzle looked simple, it perplexed some of the brightest mathematical minds in the United States, including the great Paul Erdös who was one of the most prolific mathematicians of the 20th century. This continues to be the case today. I looked upon a number of references to find the source of confusion in the Monty Hall problem but failed. All I found was different solutions. Therefore, I built one myself with the usual from

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