You are an expert Verilog hardware designer working on a complete FPGA or ASIC project. You are given the full source code of a Verilog project. One of the modules in the project is incomplete — its implementation is missing and marked with:

// >>> Module Implementation Begin

// <<< Module Implementation End

Your task is to complete the missing implementation so that the entire project functions correctly. You must infer what the missing module or logic is supposed to do by analyzing the rest of the codebase: module names, signal connections, instantiations, comments, and usage patterns.

Follow these rules:

1. Only generate Verilog code to go between the `// >>> Module Implementation Begin` and `// <<< Module Implementation End` comments.
2. Use Verilog-2001 syntax. Ensure the code is synthesizable.
3. Assume the goal is a working, integrated hardware design — your code must make the whole system function as intended.
4. Analyze the naming, I/O ports, and how the module is instantiated or used in other parts of the project.
5. Implement correct behavior based on design context. Do not guess randomly — reason it out.
6. Avoid vendor-specific features unless explicitly required.
7. Do not output comments, explanation, or anything outside the required code region unless explicitly asked.

Your output should contain **only the Verilog code** that fits inside the marked region.

/*
 * Copyright (c) 2024 Andrea Murillo Martinez & Jaeden Chang, BM
 * SPDX-License-Identifier: Apache-2.0
 */

module tt_um_murmann_group (
    input  wire [7:0] ui_in,     // Dedicated inputs
    output wire [7:0] uo_out,    // Dedicated outputs
    input  wire [7:0] uio_in,    // IOs: Input path
    output wire [7:0] uio_out,   // IOs: Output path
    output wire [7:0] uio_oe,    // IOs: Enable path (active high: 0=input, 1=output)
    input  wire       ena,       // Will go high when the design is enabled
    input  wire       clk,       // Clock
    input  wire       rst_n      // Reset (active low)
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule



module decimation_filter 
    #(parameter OUTPUT_BITS = 16, // Bit-width of output
      parameter M = 16            // Decimation factor
    )(
    input  wire clk,                // Clock
    input  wire reset,              // Reset
    input  wire X,                  // Input data from ADC
    input  wire type_dec,           // DSM type for decimation (0 = Type 1, 1 = Type 2)
    input  wire global_reset,       // Global reset, evaluated only at t = 0
    output reg [OUTPUT_BITS-1:0] Z  // Decimated output data
);

    // Integrator stage register
    reg [OUTPUT_BITS-1:0] input_accumulator;
    reg [OUTPUT_BITS-1:0] Y;

    // Comb stage registers
    reg [OUTPUT_BITS-1:0] comb_1;
    reg [OUTPUT_BITS-1:0] comb_2;

    // Decimation counter register
    reg [6:0] decimation_count;

    // Previous reset state to detect edges
    reg reset_d;

    // Previous decimation type to reset if it changes
    reg type_dec_d;

    always @(posedge clk) begin
        if (global_reset) begin
            // Global initialization at t=0
            input_accumulator <= 0;
            Y <= 0;
            comb_1 <= 0;
            comb_2 <= 0;
            decimation_count <= 0;
            Z <= 0;
            reset_d <= 0;
            type_dec_d <= type_dec;
        end else begin
            // Detect positive edge of reset or type change
            if ((reset && !reset_d) || (type_dec_d ^ type_dec)) begin
                if ((type_dec_d ^ type_dec) || type_dec) begin
                    Z <= 0;
                end else begin
                    // Type 1: Incremental DSM, output when reset is active
                    Z <= Y;
                end

                // Reset internal states
                input_accumulator <= 0;
                Y <= 0;
                comb_1 <= 0;
                comb_2 <= 0;
                decimation_count <= 0;

            end else begin
                // Integrator stage (accumulate input samples)
                input_accumulator <= input_accumulator + {15'b0, X};
                Y <= Y + input_accumulator;

                // Decimation control based on type
                if (type_dec) begin
                    // Type 2: Regular DSM with decimation control
                    if (decimation_count == M - 1) begin
                        // Comb stage (only every M cycles)
                        comb_1 <= Y;
                        comb_2 <= comb_1;
                        Z <= comb_1 - comb_2;

                        // Reset integrators and decimation counter
                        input_accumulator <= 0;
                        Y <= 0;
                        decimation_count <= 0;
                    end else begin
                        // Increment decimation counter
                        decimation_count <= decimation_count + 1;
                    end
                end 
            end
            // Update reset_d to detect the next reset edge
            reset_d <= reset;
            // Update type_dec_d to detect change
            type_dec_d <= type_dec;
        end
    end
endmodule


Reference solution:
rtl/generated.v: 
    // Prevent warnings for unused inputs
    wire _unused = &{ui_in[7:3], uio_in[7:0], ena, 1'b0};

    // Declare wires
    wire X;
    wire type_dec;
    wire global_reset;

    // ADC 1-bit input
    assign X = ui_in[0];

    // Type of decimation (incremental or regular delta-sigma modulator)
    // 0: Incremental DSM (type 1)
    // 1: Regular DSM (type 2)
    assign type_dec = ui_in[1];

    // Global reset, evaluated at t = 0
    assign global_reset = ui_in[2];

    // Output of the decimation filter (Z in decimation_filter module)
    wire [15:0] decimation_output;

    // Enable all uio pins for output
    assign uio_oe = 8'b11111111;

    // Assign most significant 8 bits to the dedicated output pins
    assign uo_out = decimation_output[15:8];

    // Assign least significant 8 bits to the general-purpose IO pins
    assign uio_out = decimation_output[7:0];

    // Instantiate the decimation filter
    decimation_filter my_decimation_filter(
        .clk(clk),
        .reset(~rst_n),
        .X(X),
        .type_dec(type_dec),
        .global_reset(global_reset),
        .Z(decimation_output)
    );