Showing raised cosine and FFT.

Raised cosine is displayed in an interactive JavaFX GUI. The beta
value can be dyanmically adjusted from 0 to 1 and an FFT displays
the spectral impact to the most recent adjustment.
A low-pass filter can replace the raised cosine FIR filter to show
the difference between the two.

README.md

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+# Speed Graph with Adjustable Raised Cosine Filter
+
+This JavaFX application demonstrates the concept of a raised cosine filter applied to signal data, visualized in a dynamic graph. The user can control two key parameters:
+
+## Key Features
+
+### 1. Speed (Vertical Slider)
+- Controlled via a vertical slider.
+- This parameter determines the value of the signal (represented as speed) at each time step.
+- The slider's range is from -100 to 100.
+
+### 2. Beta (Roll-off Factor - Horizontal Slider)
+- Controlled via a horizontal slider.
+- Adjusts the roll-off factor (β) of the raised cosine filter.
+- A higher beta value produces smoother transitions in the signal.
+- The range is from 0 (sharp transitions) to 1 (smooth transitions).
+
+## Graph Display
+The graph displays two series:
+- **Original Speed**: Represents the unfiltered signal, directly derived from the speed slider.
+- **Filtered Speed (Raised Cosine)**: Represents the signal after it has been processed by a raised cosine filter, smoothing transitions based on the roll-off factor (beta).
+
+### Dynamic Graph
+- The graph updates in real-time, continuously adding new points. 
+- It provides a sliding window effect, always showing the latest data over a fixed time window.
+  
+### Pre-populated Graph
+- The graph is filled with zeros at startup, ensuring smoother transitions immediately.
+
+### Adjustable Raised Cosine Filter
+- The filtered speed is processed using a raised cosine filter.
+- The filter is adjustable via the beta slider to simulate smooth signal transitions.
+
+### Signal Smoothing with FIR Filtering
+- The raised cosine filter is implemented as a finite impulse response (FIR) filter.
+- The coefficients (taps) of the filter are dynamically generated and applied to the input signal for smoothing.
+
+### Live Beta Value Display
+- The current beta value is displayed dynamically as the slider is adjusted.
+- This helps the user visualize the filter’s effect in real-time.
+
+## Technologies Used
+- **JavaFX**: For the graphical user interface, including sliders and real-time graph.
+- **JFreeChart**: For rendering the dynamic line chart visualizing signal data.
+
+## Purpose
+This application simulates how a raised cosine filter can smooth transitions in a signal, with user-controllable parameters. It's particularly relevant for digital communication systems, where pulse shaping is critical for minimizing bandwidth and reducing inter-symbol interference (ISI).