## Direct Digital Synthesizer (DDS)

A Direct Digital Synthesizer (DDS) is an integral part of all modern communication systems. It is a technique to produce a desired waveform, usually a sinusoid, through employing digital signal processing algorithms. As an example, in the transmitter (Tx) of a digital communication system, a Local Oscillator (LO) is required to generate a carrier sinusoid that upconverts the modulated signal to its allocated frequency in the spectrum. On the receive (Rx) side, another local oscillator downconverts this high frequency signal to baseband for further processing. Such a process is shown in the Tx and Rx block diagrams of a Quadrature

## 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)

## Spectral Shift without any Multiplications

One of the great advantages of Digital Signal Processing (DSP) is an unexpected simplification of operations in seemingly complicated scenarios. See the Cascade Integrator Comb (CIC) filters for how to accomplish the task of sample rate conversion along with filtering with minimal resources. As another example, in wireless communications and many other applications, a frequency translation is often required in which the spectrum of a signal centered at a particular frequency needs to be moved to another frequency. From the properties of Fourier Transform, a shift by frequency $\omega_0=2\pi F_0$ requires sample-by-sample multiplication with a complex sinusoid $e^{j\omega_0 t}$. \[