The transformation of waveforms using simple passive components like resistors and capacitors illustrates the power of analog signal processing. Specifically, converting a square wave into a triangular waveform involves smoothing the sharp transitions of the square wave, a process achievable through careful RC filtering.

**Objective**

The aim of this experiment is to utilize an RC filter with a specific time constant to convert a square wave into a waveform that closely resembles a triangular wave. By analyzing the signal's frequency components and comparing them to an ideal triangular waveform, we aim to explore the principles of waveform transformation and signal analysis.

**Materials and Setup**

- Square wave oscillator (e.g., an OpAmp multivibrator circuit)
- RC filter components: 10 kOhm resistor and 10 nF capacitor
- Red Pitaya or equivalent for signal generation, measurement, and analysis
- Tools for Discrete Fourier Transform (DFT) analysis (software or Red Pitaya applications)

**Circuit Assembly**

**Square Wave Generation:**Start with a square wave oscillator circuit, ensuring it produces a stable square wave at the base frequency of interest.**RC Filter Integration:**Incorporate an RC filter (10 kOhm resistor and 10 nF capacitor) into the square wave's output path to initiate waveform smoothing.

**Conducting the Experiment**

**Waveform Transformation:**Observe the transformation of the square wave into a triangular-like waveform after passing through the RC filter, paying close attention to the waveform's corners and overall shape.**Signal Analysis:**Utilize DFT analysis to examine the frequency components of the transformed signal. Convert the spectral peaks from dBm to volts to compare with the theoretical amplitudes of an ideal triangular waveform.

**Analysis and Observations**

**Triangular Waveform Characteristics:**The resulting waveform, while not a perfect triangular wave, exhibits characteristics close to one due to the RC filter's time constant being significantly greater than the oscillator's base frequency.**Spectral Analysis:**The analysis reveals that the waveform consists of the base frequency and odd harmonics, similar to a square wave, but with amplitudes following a specific pattern as described by the given equation.

**Relevant Equations**

The relationship between voltage (*U*) and power in dBm ($P_{dbm}$) is proportional and can be expressed as:

Triangular waveforms consist of base frequency and odd multiples (same as square wave) with amplitudes of those spectral following this equation:

$a_n = \frac{2 \cdot amplitiude}{n \cdot \pi} sin(\frac{n \cdot \pi}{2}) , n=[1,2,5,...)$where *n *represents the harmonic order, and *amplitude *is the peak amplitude of the waveform.

**Conclusion**

This experiment demonstrates the feasibility of transforming a square wave into a triangular-like waveform through RC filtering, showcasing the practical application of analog signal processing techniques. By analyzing the transformed signal and comparing its spectral components to those of an ideal triangular waveform, we gain insights into the nature of waveform shaping and the impact of filtering on signal characteristics. This exploration not only reinforces the theoretical foundations of waveform analysis but also provides a hands-on approach to understanding and applying signal processing concepts in real-world scenarios.