Exercise 3.74

# Zero crossings

Alyssa P. Hacker is designing a system to process signals coming from physical sensors. One important feature she wishes to produce is a signal that describes the zero crossings of the input signal. That is, the resulting signal should be + 1 whenever the input signal changes from negative to positive, - 1 whenever the input signal changes from positive to negative, and 0 otherwise. (Assume that the sign of a 0 input is positive.) For example, a typical input signal with its associated zero-crossing signal would be

``````
...1  2  1.5  1  0.5  -0.1  -2  -3  -2  -0.5  0.2  3  4 ...
...0  0   0   0    0    -1   0   0   0    0    1   0  0 ...
``````

In Alyssa's system, the signal from the sensor is represented as a stream sense-data and the stream zero-crossings is the corresponding stream of zero crossings. Alyssa first writes a procedure sign-change-detector that takes two values as arguments and compares the signs of the values to produce an appropriate 0, 1, or - 1. She then constructs her zero-crossing stream as follows:

``````(define (make-zero-crossings input-stream last-value)
(cons-stream
(sign-change-detector (stream-car input-stream) last-value)
(make-zero-crossings (stream-cdr input-stream)
(stream-car input-stream))))

(define zero-crossings (make-zero-crossings sense-data 0))
``````

Alyssa's boss, Eva Lu Ator, walks by and suggests that this program is approximately equivalent to the following one, which uses the generalized version of stream-map from exercise 3.50:

``````(define zero-crossings
(stream-map sign-change-detector sense-data <expression>))
``````

Complete the program by supplying the indicated <expression>.

Nobody's finished this exercise yet. You'll be the first!