This chapter explores analog signals, their characteristics, and how they differ from digital signals. Analog signals are continuous-time signals that can take any value within a range.
- Continuous Nature: Analog signals vary smoothly over time
- Infinite Values: Can take any value within a range (unlike digital's discrete values)
- Physical World: Most natural phenomena produce analog signals (sound, light, temperature)
- Definition: The maximum displacement from the equilibrium position
- Measurement: Typically measured in volts, decibels, or other units
- Significance: Determines signal strength or intensity
- Definition: Number of complete cycles per second
- Unit: Hertz (Hz), where 1 Hz = 1 cycle/second
- Formula: f = 1/T (frequency is inverse of period)
- Common Ranges:
- Audio: 20 Hz - 20 kHz
- Radio: kHz - GHz
- Light: ~400-790 THz
- Definition: Time taken for one complete cycle
- Unit: Seconds (or milliseconds, microseconds)
- Formula: T = 1/f (period is inverse of frequency)
- Definition: Position of a waveform relative to a reference point
- Measurement: Degrees (0°-360°) or radians (0-2π)
- Phase Shift: Difference in phase between two signals
- Formula: y(t) = A × sin(2πft + φ)
- A = amplitude
- f = frequency
- t = time
- φ = phase shift
- Properties: Smooth, periodic, fundamental waveform in nature
- Square Wave: Alternates between two levels
- Triangle Wave: Linear rise and fall
- Sawtooth Wave: Linear rise, sharp drop (or vice versa)
By the end of this chapter, you should be able to:
- Define analog signals and their characteristics
- Calculate frequency, period, and wavelength
- Understand the relationship between frequency and period
- Analyze amplitude and phase of signals
- Work with sine waves and their properties
- Distinguish between analog and digital representations
Run the interactive example:
python ch02_analog_signals.py- Frequency and Period Calculations: Computing f = 1/T and T = 1/f
- Sine Wave Generation: Creating sinusoidal signals mathematically
- Amplitude Effects: How amplitude affects signal strength
- Phase Shift: Demonstrating phase differences between signals
- Signal Sampling: Taking discrete samples of continuous signals
- Common Frequencies: Examples from audio, radio, and other domains
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CHAPTER 2: Analog Signals
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--- Example 1: Frequency and Period Relationship ---
For a signal with frequency 1000 Hz:
Period T = 1/f = 1/1000 = 0.001 seconds (1.0 ms)
For a signal with period 0.002 seconds:
Frequency f = 1/T = 1/0.002 = 500 Hz
...
- Microphones: Convert sound (analog) to electrical signals
- Speakers: Convert electrical signals to sound waves
- Music: Pure tones are sine waves at specific frequencies
- Voice: Complex combination of multiple frequencies
- AM Radio: Amplitude Modulation (varies amplitude)
- FM Radio: Frequency Modulation (varies frequency)
- Broadcasting: Carrier waves at specific frequencies
- Temperature: Thermocouples produce analog voltage
- Light: Photodiodes generate current proportional to light intensity
- Pressure: Strain gauges output analog voltage
- ECG/EKG: Heart electrical activity (analog waveform)
- EEG: Brain wave patterns
- Ultrasound: High-frequency sound waves
| Aspect | Analog | Digital |
|---|---|---|
| Values | Continuous (infinite) | Discrete (finite) |
| Representation | Smooth curves | Step-like levels |
| Noise Susceptibility | High (accumulates) | Low (can be corrected) |
| Storage | Difficult (degrades) | Easy (exact copies) |
| Processing | Limited | Extensive (computers) |
| Real World | Natural signals | Computer systems |
Q: Why do we convert analog signals to digital?
A: Digital signals are easier to store, process, transmit, and reproduce without degradation. Computers can only work with discrete values.
Q: What is sampling?
A: Sampling is the process of converting analog signals to digital by taking measurements at regular intervals.
Q: What's the Nyquist theorem?
A: To accurately represent an analog signal digitally, you must sample at least twice the highest frequency present in the signal.
Q: Can we perfectly reproduce analog signals from digital?
A: With sufficient sampling rate and bit depth, we can get very close, but there's always some information loss in the analog-to-digital conversion.
Frequency: f = 1/T (Hz)
Period: T = 1/f (seconds)
Angular Frequency: ω = 2πf (rad/s)
Wavelength: λ = v/f (meters, where v = wave speed)
Sine Wave: y(t) = A·sin(2πft + φ)
where: A = amplitude
f = frequency
t = time
φ = phase (radians)
- Analog signals are continuous and can take infinite values within a range
- Frequency and period are inversely related: f = 1/T
- Amplitude, frequency, and phase are the three main characteristics
- 🎵 Natural phenomena (sound, light, temperature) are inherently analog
- Digital systems require converting analog signals through sampling
- Sine waves are the fundamental building blocks of complex signals
- Calculate the period of a 440 Hz signal (musical note A)
- What is the frequency of a signal with a period of 50 microseconds?
- Draw a sine wave and label its amplitude, period, and frequency
- If a signal has frequency 1 kHz and is phase-shifted by 90°, write its equation
- Explain why analog audio recordings degrade over time but digital recordings don't
- Explore digital signals in Chapter 3
- Learn about analog-to-digital conversion
- Study Fourier analysis (any signal can be decomposed into sine waves)
- Investigate sampling theory and the Nyquist-Shannon theorem
Course Navigation:
← Previous: Chapter 1 - Signals and Number Systems | Next: Chapter 3 - Digital Signals →