A discrete-time FM demodulator block diagram with atan2 and derivative filter
DSP / Wireless/SDR

Frequency Modulation (FM) and Demodulation Using DSP Techniques

Frequency Modulation (FM) is as old as the history of wireless communications itself. The past few decades saw the rise of digital signal processing in all spheres of life that pervaded even the implementation of analog modulation schemes. Today many of the FM systems are built using discrete-time techniques instead of the conventional circuitry as described below. Frequency Modulation In digital communications, data is sent through altering a characteristic of an electromagnetic wave such as amplitude, frequency or phase in discrete steps (e.g., $M$ number of levels). Such systems are known as Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK)

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Spectrum of the cascade of CIC filters with a wideband compensation filter for rate change factor 10, unit differential delay and 4 stages
DSP / Wireless/SDR

Cascaded Integrator Comb (CIC) Filters – A Staircase of DSP

In olden days, people used to have lots of kids. A famous Urdu satirist once wrote: "It has been observed that the last kid is usually the most mischievous of them all. Therefore, there should be no last kid in a family!" I remembered this line today because I have observed that starting a write-up is the most difficult task of them all. Therefore, there is no introductory paragraph in this article. Suffice it to say that this is the only topic I have found that takes you from a very small first step (just two additions) to really advanced

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The image frequency problem of a superheterodyne Rx
Wireless/SDR

The Heterodyne Principle and the Superheterodyne Receiver

During World War I, Edwin Howard Armstrong invented the superheterodyne Rx as an alternative to the Tuned Radio Frequency (TRF) receivers that moved a tunable filter to the desired signal. His purpose was to overcome their limitations in regard to selectivity and sensitivity. To understand the principle of a heterodyne receiver, a pictorial representation is of utmost importance. While this is generally true for all concepts, there are specific issues of spectral translations in receiver architectures that require nice and clear figures. This is how I proceed below. The Heterodyne Principle Instead of employing a tunable bandpass filter that is

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A basic chirp with real and imaginary signals
Wireless/SDR

Understanding LoRa PHY (Long-Range Physical Layer)

LoRa PHY (Long-Range Physical Layer) is a very exciting communication technique based on Chirp Spread Spectrum (CSS) modulation mixed with Frequency Shift Keying (FSK). It is a proprietary physical layer methodology patented by Semtech. On the other hand, LoRaWAN is a Low Power Wide Area Network (LPWAN) protocol that is built on top of LoRa PHY. Some of the benefits of LoRa are resistance to multipath fading and Doppler effect, robustness against narrowband interference and jamming, low RF power consumption owing to the constant envelope signal, computationally simple from signal processing perspective, long-range transmission and reception, and inherent ranging capability

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Data symbols riding on the subcarriers experience a rotation due to residual carrier frequency offset and sampling frequency offset
Wireless/SDR

Effect of a Sampling Clock Offset on an OFDM Waveform

In an earlier article on the impact of a sampling clock offset on a single-carrier waveform, we explained the nature of a Sampling Clock Offset (SCO), i.e., a difference in sampling clock frequency between the Tx and the Rx. This is also known as a symbol timing frequency offset. The meaning of a sampling clock offset for a slow Rx clock that skips some samples within an interval is visually demonstrated in the figure below. In the context of OFDM systems, a previous article describes how the normalized Carrier Frequency Offset (CFO) and the normalized Symbol Timing Offset (STO) affect

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