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Likelihood Ratio Receiver Formula:
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The Likelihood Ratio Receiver is a measure of probability that compares the likelihood of a signal occurring with noise versus noise alone. It is used in signal detection theory to quantify the probability of occurrence of one event relative to another.
The calculator uses the Likelihood Ratio Receiver formula:
Where:
Explanation: The formula calculates the ratio between the probability density of signal with noise and the probability density of noise alone, providing a measure of signal detection performance.
Details: The Likelihood Ratio Receiver is crucial in signal detection theory, statistical decision making, and pattern recognition systems. It helps quantify how much more likely a signal is present compared to noise alone.
Tips: Enter the probability density function values for signal with noise (Psn) and noise alone (Pn). Both values must be positive numbers greater than zero.
Q1: What does a Likelihood Ratio Receiver value indicate?
A: A value greater than 1 indicates the signal is more likely to be present, while a value less than 1 suggests noise is more likely.
Q2: How is this different from other likelihood ratios?
A: This specific ratio focuses on signal detection scenarios where we compare signal+noise probability against noise-only probability.
Q3: What are typical values for Psn and Pn?
A: These are probability density values that typically range between 0 and 1, representing the likelihood of specific signal or noise values occurring.
Q4: Can this calculator handle very small probability values?
A: Yes, the calculator can handle very small values, but extremely small values may approach computational limits.
Q5: What applications use Likelihood Ratio Receivers?
A: This concept is used in radar systems, medical diagnostics, communication systems, and any field involving signal detection and statistical decision theory.