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>.
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