Introduction to Digital Filters

Introduction

In the field of digital signal processing (DSP), “filtering” is one of the oldest and most classical topics; filter design and optimization constitute a key research area within DSP. Filtering plays a vital role in IoT systems, serving as a foundational technique for both sensing and communication signal processing. This chapter introduces the fundamental principles and functions of filters, with emphasis on helping readers understand the characteristics and differences among various filter types—and enabling them to select appropriate filters for different application requirements, thereby satisfying the needs of most practical IoT applications and research. For clarity and accessibility, many explanations in this chapter adopt intuitive, informal descriptions.

Filtering primarily comprises analog filtering and digital filtering. Analog filtering processes physical signals directly—typically by designing circuits—to manipulate signal frequency content, usually by attenuating or eliminating components outside a specified frequency band. For example, an RLC circuit composed of resistors, capacitors, and inductors can selectively suppress certain signal components. Digital filtering, by contrast, operates on sampled and quantized signals. In real-world communication systems, both analog and digital filtering are commonly employed together to achieve superior overall filtering performance. Due to space constraints, this book does not elaborate on analog filtering.

The function of digital filters can generally be summarized in two aspects: signal restoration and signal separation.
Signal restoration refers to the ability of a filter to recover a distorted signal, partially reconstructing the original waveform characteristics. For instance, when processing audio signals captured by low-quality recording equipment, digital filtering can eliminate noise spikes or DC interference, yielding an output waveform that more closely resembles the original sound.
Signal separation, on the other hand, refers to the ability of a filter to isolate a target signal from overlapping, interfering, or noisy components. For example, in fetal electrocardiogram (ECG) detection, the acquired ECG signal contains superimposed cardiac activity from both fetus and mother; digital filtering can separate the fetal ECG component from the maternal one, thus achieving signal separation.

These two primary functions of digital filtering correspond precisely to the two distinct information-carrying modes of signals: time-domain modulation and frequency-domain modulation.
Time-domain modulation encodes information using waveform features such as amplitude and phase. In such cases, time-domain sampling results can be directly used to extract information—for example, astronomers analyze solar flare activity by measuring variations in solar irradiance intensity. For time-domain modulated signals, the signal restoration capability of digital filters helps recover time-domain waveform features—for instance, smoothing the signal or removing its DC component.
Frequency-domain modulation, though less intuitively accessible than time-domain modulation, fundamentally relies on distinguishing and encoding information via the frequency characteristics of periodic signals. Extracting encoded information from frequency-domain modulated signals requires first transforming the signal into the frequency domain and then analyzing its spectral energy distribution to identify the embedded information. The signal separation capability of digital filters facilitates isolating the target signal from interference or noise in the frequency domain, thereby enhancing extraction of the target signal’s spectral features.