// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("SSF-Based Detrended Synthetic Price", "SSF-DSP", overlay=false)

//@function Calculates SSF-based Detrended Synthetic Price using dual Super Smooth Filters
//@doc https://github.com/mihakralj/pinescript/blob/main/indicators/cycles/ssfdsp.md
//@param source Series to detrend
//@param period Dominant cycle period for quarter/half-cycle SSF calculation
//@returns Detrended synthetic price (difference between quarter-cycle and half-cycle SSFs)
ssfdsp(series float source, simple int period) =>
    if period <= 0
        runtime.error("Period must be greater than 0")
    int fast_period = math.max(2, int(math.round(period / 4.0)))
    int slow_period = math.max(3, int(math.round(period / 2.0)))
    float SQRT2_PI = math.sqrt(2.0) * math.pi
    float arg_fast = SQRT2_PI / float(fast_period)
    float exp_fast = math.exp(-arg_fast)
    float c2_fast = 2.0 * exp_fast * math.cos(arg_fast)
    float c3_fast = -exp_fast * exp_fast
    float c1_fast = 1.0 - c2_fast - c3_fast
    float arg_slow = SQRT2_PI / float(slow_period)
    float exp_slow = math.exp(-arg_slow)
    float c2_slow = 2.0 * exp_slow * math.cos(arg_slow)
    float c3_slow = -exp_slow * exp_slow
    float c1_slow = 1.0 - c2_slow - c3_slow
    var float ssf_fast_1 = 0.0
    var float ssf_fast_2 = 0.0
    var int prev_fast_period = 0
    var float ssf_slow_1 = 0.0
    var float ssf_slow_2 = 0.0
    var int prev_slow_period = 0
    float current = nz(source)
    float src_1 = nz(source[1], current)
    float input = (current + src_1) * 0.5
    if prev_fast_period != fast_period
        ssf_fast_1 := input
        ssf_fast_2 := input
        prev_fast_period := fast_period
    if prev_slow_period != slow_period
        ssf_slow_1 := input
        ssf_slow_2 := input
        prev_slow_period := slow_period
    float ssf_fast = c1_fast * input + c2_fast * ssf_fast_1 + c3_fast * ssf_fast_2
    ssf_fast_2 := ssf_fast_1
    ssf_fast_1 := ssf_fast
    float ssf_slow = c1_slow * input + c2_slow * ssf_slow_1 + c3_slow * ssf_slow_2
    ssf_slow_2 := ssf_slow_1
    ssf_slow_1 := ssf_slow
    ssf_fast - ssf_slow

// ---------- Main loop ----------

// Inputs
i_source = input.source(hlc3, "Source")
i_period = input.int(40, "Dominant Cycle Period", minval=4, maxval=200, 
  tooltip="Dominant cycle period. Quarter-cycle and half-cycle SSFs calculated from this value.")

// Calculation
ssfdsp_val = ssfdsp(i_source, i_period)

// Plot
plot(ssfdsp_val, "SSF-DSP", color=color.yellow, linewidth=2)
hline(0, "Zero Line", color=color.gray, linestyle=hline.style_solid)