Signal Operations: Amplitude Domain
## Why Time-Domain Operations Matter
Signal Operations: Amplitude Domain
Why Time-Domain Operations Matter
Before we transform signals to frequency domains or filter them, we manipulate them in the time domain. These operations are the building blocks of all DSP systems—delay lines, filters, interpolators, decimators, and more.
Every discrete-time signal operation falls into two categories:
- Amplitude (y-axis) operations: Addition, subtraction, multiplication, scaling
- Time (x-axis) operations: Shifting, scaling, reversal (folding)
Amplitude Operations (Vertical Axis)
Given two sequences $x_1[n]$ and $x_2[n]$:
| Operation | Formula | Block Diagram |
|---|---|---|
| Addition | $y[n] = x_1[n] + x_2[n]$ | Summer |
| Subtraction | $y[n] = x_1[n] - x_2[n]$ | Subtractor |
| Multiplication | $y[n] = x_1[n] \cdot x_2[n]$ | Modulator |
| Amplitude Scaling | $y[n] = \alpha x[n]$ | Gain block |
Applications:
- Addition: Mixing audio signals, combining sensor readings
- Multiplication: Amplitude modulation (AM), gating/windowing
- Scaling: Volume control, normalization
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